unit 2images.pcmac.org/.../2016...geometry_pacing_guide.docx · web view1. [g-co.1] know precise...

Huntsville City Schools - Instructional Guide

2016 – 2017

Course: Geometry Grades: 9-11

Color Clarifications:

Green has to do with pacing/timing/scheduling of materials.Pink has to do with differentiating between Regular Geometry and Honors Geometry.Yellow places emphasis on a particular portion of a standard pertinent to that teaching unit.Blue signifies that the standard is a power standard.

Table of Contents:(If you are viewing this document in Microsoft Word, hold the “Control” key and click on the Unit you want to view in order to go directly to that unit. If you are viewing the document as a PDF, just click on the link.)Unit 1 - First 9-weeks......................................................................................................................................................................................................2

Unit 2 - First 9-weeks......................................................................................................................................................................................................4

Unit 3 - First 9-weeks......................................................................................................................................................................................................6

Unit 4 - Second 9-weeks.................................................................................................................................................................................................9

Unit 5 - Second 9-weeks...............................................................................................................................................................................................11

Unit 6a - Second 9-weeks..............................................................................................................................................................................................13

Unit 6b - Third 9-weeks................................................................................................................................................................................................14

Unit 7 - Third 9-weeks..................................................................................................................................................................................................15

Unit 8 - Third 9-weeks..................................................................................................................................................................................................17

Unit 10a - Third 9-weeks...............................................................................................................................................................................................20

Unit 10b - Fourth 9-weeks.............................................................................................................................................................................................22

Unit 12 - Fourth 9-weeks...............................................................................................................................................................................................24

Unit 11 - Fourth 9-weeks...............................................................................................................................................................................................26

Unit 9 - Fourth 9-weeks.................................................................................................................................................................................................28

Geometry Vocabulary

CCRS Standard Vocabulary CCRS Standard Vocabulary1. [G-CO.1] Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Point Line Segment Angle ∙ ∙ ∙ ∙Perpendicular line Parallel line ∙ ∙Distance Arc length Ray Vertex ∙ ∙ ∙ ∙Endpoint Plane Collinear ∙ ∙ ∙Coplanar Skew∙ ∙

22. [G-SRT.10] (+) Prove the Laws of Sines and Cosines and use them to solve problems.

Law of Sines Law of Cosines∙ ∙

2. [G-CO.2] Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

Transformation Reflection ∙ ∙Translation Rotation Dilation ∙ ∙ ∙Isometry Composition Horizontal ∙ ∙ ∙

stretch Vertical stretch Horizontal ∙ ∙shrink Vertical shrink Clockwise ∙ ∙

Counterclockwise Symmetry ∙ ∙Preimage Image∙ ∙

23. [G-SRT.11] (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

Law of Sines Law of Cosines ∙ ∙Transit Resultant force∙ ∙

3. [G-CO.3] Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Transformation reflection ∙ ∙translation rotation dilation ∙ ∙ ∙isometry composition horizontal ∙ ∙ ∙

stretch vertical stretch horizontal ∙ ∙shrink vertical shrink clockwise ∙ ∙

counterclockwise symmetry ∙ ∙trapezoid square rectangle ∙ ∙ ∙regular polygon parallelogram ∙ ∙mapping preimage image∙ ∙ ∙

24. [G-C.1] Prove that all circles are similar.

Diameter Radius Circle Similar∙ ∙ ∙ ∙

4. [G-CO.4] Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

Transformation Reflection ∙ ∙Translation Rotation Dilation ∙ ∙ ∙Isometry Composition Clockwise ∙ ∙ ∙Counterclockwise Preimage ∙ ∙Image∙

25. [G-C.2] Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where

Central angles Inscribed angles ∙ ∙Circumscribed angles Chord ∙ ∙Circumscribed Tangent ∙ ∙Perpendicular∙

the radius intersects the circle.5. [G-CO.5] Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

Transformation Reflection ∙ ∙Translation Rotation Dilation∙ ∙ ∙

26. [G-C.3] Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

Construct Inscribed and ∙ ∙circumscribed circles of a triangle

Quadrilateral inscribed in a circle ∙Opposite angles Consecutive ∙ ∙

angles Incenter Circumcenter ∙ ∙Orthocenter Angle bisector ∙ ∙Altitude Median of a triangle ∙ ∙Centroid∙

6. [G-CO.6] Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

Rigid motions Congruence∙ ∙ 27. [G-C.4] (+) Construct a tangent line from a point outside a given circle to the circle.

Tangent line Tangent Point of ∙ ∙ ∙tangency Perpendicular∙

7. [G-CO.7] Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

Corresponding sides and angles ∙Rigid motions If and only if∙ ∙

28. [G-C.5] Derive, using similarity, the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Similarity Constant of ∙ ∙proportionality Sector Arc ∙ ∙

Derive Arc length Radian ∙ ∙ ∙measure Area of sector Central ∙ ∙angle

8. [G-CO.8] Explain how the criteria for triangle congruence, angle-side-angle (ASA), side-angle-side (SAS), and side-side-side (SSS), follow from the definition of congruence in terms of rigid motions.

Triangle congruence Angle-Side-∙ ∙Angle (ASA) Side-Angle-Side (SAS) ∙

Side-Side-Side (SSS)∙

29. [G-GPE.1] Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Pythagorean theorem Radius∙ ∙

9. [G-CO.9] Prove theorems about lines and angles. Theorems include vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

Same side interior angle ∙Consecutive interior angle Vertical ∙ ∙

angles Linear pair Adjacent angles ∙ ∙Complementary angles ∙Supplementary angles ∙Perpendicular bisector Equidistant ∙ ∙Theorem Proof Prove Transversal∙ ∙ ∙ Alternate interior angles ∙Corresponding angles∙

30. [G-GPE.4] Use coordinates to prove simple geometric theorems algebraically. Example: Prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

Simple geometric theorems ∙Simple geometric figures∙

10. [G-CO.10] Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180o, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, the medians of a triangle meet at a point.

Interior angles of a triangle ∙Isosceles triangles Equilateral ∙ ∙

triangles Base angles Median ∙ ∙Exterior angles Remote interior ∙ ∙

angles Centroid∙

31. [G-GPE.5] Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Parallel lines Perpendicular lines ∙ ∙Slope∙

11. [G-CO.11] Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Parallelograms Diagonals Bisect∙ ∙ ∙ 32. [G-GPE.6] Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Directed line segment Partitions ∙ ∙Dilation Scale factor∙ ∙

12. [G-CO.12] Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software, etc. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Construction Compass∙ ∙ 33. [G-GPE.7] Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*

Coordinates Cartesian coordinate∙ ∙ system Perimeter Area Triangle∙ ∙ ∙

Rectangle∙

13. [G-CO.13] Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Construct Inscribed Hexagon ∙ ∙ ∙Regular∙

34. [G-GMD.5] Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. (Alabama)

Area Perimeter Inscribed ∙ ∙ ∙polygons Circumscribed polygons ∙

Regular polygons Apothem ∙ ∙Coordinates Vertices Height ∙ ∙ ∙Radius Diameter Perpendicular ∙ ∙ ∙

bisector Distance Midpoint ∙ ∙Slope Classification of polygons ∙ ∙Cartesian coordinate system∙

14. [G-SRT.1] Verify experimentally the properties of dilations given by a center and a scale factor. A dilation ∙takes a line not passing through the center of the dilation to a parallel line and leaves a line passing through the center unchanged. The dilation of a ∙line segment is longer or shorter in the ratio given by the scale factor.

Dilations Center Scale factor∙ ∙ ∙ 35. [G-GMD.1] Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments.

Dissection arguments Cavalieri's ∙ ∙Principle Cylinder Pyramid Cone∙ ∙ ∙

Ratio Circumference ∙ ∙Parallelogram Limits Conjecture∙ ∙ ∙ Cross-section∙

15. [G-SRT.2] Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. (Alabama)Example 1: Image Given the two triangles above, show that they are similar. 4/8 = 6/12 They are similar by SSS. The scale factor is equivalent. Example 2: Image Show that the two triangles are similar. Two corresponding sides are proportional and the included angle is congruent. (SAS similarity)

Similarity transformation Similarity∙ ∙ Proportionality Corresponding ∙ ∙

pairs of angles Corresponding pairs ∙of sides

36. [G-GMD.3] Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*

Cylinder Pyramid Cone Sphere∙ ∙ ∙ ∙

16. [G-SRT.3] Use the properties of similarity transformations to establish the angle-angle (AA) criterion for two triangles to be similar.

Angle-Angle (AA) criterion∙ 37. [G-GMD.6] Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama) *

Volume Surface area Similar ∙ ∙ ∙Ratio Dimensions∙ ∙

17. [G-SRT.4] Prove theorems about triangles. Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

Theorem Pythagorean Theorem∙ ∙ 38. [G-GMD.4] Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

Two-dimensional cross-sections ∙Two-dimensional objects Three-∙ ∙

dimensional objects Rotations ∙Conjecture∙

18. [G-SRT.5] Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Congruence and similarity criteria ∙for triangles

39. [G-MG.1] Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*

Model∙

19. [G-SRT.6] Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle leading to definitions of trigonometric ratios for acute angles.

Side ratios Trigonometric ratios ∙ ∙Sine Cosine Tangent Secant ∙ ∙ ∙ ∙Cosecant Cotangent∙ ∙

40. [G-MG.2] Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, British Thermal Units (BTUs) per cubic foot).*

Density∙

20. [G-SRT.7] Explain and use the relationship between the sine and cosine of complementary angles.

Sine Cosine Complementary ∙ ∙ ∙angles

41. [G-MG.3] Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).*

Geometric methods Design ∙ ∙problems Typographic grid system∙

21. [G-SRT.8] Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*

Angle of elevation Angle of ∙ ∙depression

42. [S-MD.6] (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

Fair decisions Probability Fair ∙ ∙ ∙decisions Random∙

43. [S-MD.7] (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). (Alabama)Example: Image What is the probability of tossing a penny and having it land in the non-shaded region? Geometric Probability is the Non-Shaded Area divided by the Total Area.

Probability∙

Unit 1 - First 9-weeks

Standard “I Can” Statements * ResourcesPacing

Recommendation / Date(s) Taught

First 9-weeksUnit 1: Tools for Geometry 12 daysThis unit corresponds well with Pearson Geometry Chapter 1, with the first portion of the unit giving emphasis to the building of proper vocabulary and symbology, while the second portion is emphasizing the application points, lines, and planes, as well as the other learned vocabulary. ALCOS #1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [G-CO1]

Pearson: 1.2-1.5 IXL:B.1,C.1,D.1LTF:

Throughout the unit.5 days

ALCOS #32. Find the point on a directed line segment between two given points that partitions the segment in a given ratio. [G-GPE6]

Pearson: 1.7 (Problem 46)IXL:LTF:

2 days

ALCOS #12. Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [G-CO12]

Pearson: 1.6 IXL:B.9,C.6,C.7LTF:

1 day

ALCOS #30. Use coordinates to prove simple geometric theorems algebraically. [G-GPE4]

Pearson:1.7 IXL:B.7LTF:

ALCOS #33. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* [G-GPE7]

Pearson: 1.7-1.8 IXL:LTF:

ALCOS #39. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [G-MG1]

Pearson: 1.8 IXL:LTF: Infinity in Geometry (This lesson shows the derivation of the area of a circle based on the formula for circumference, and cutting the circle into tiny sectors.)

2 days

ALCOS #40. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, British Thermal Units (BTUs) per cubic foot). [G-MG2]

Pearson: 1.8 IXL:LTF:

(Quality Core) D.1.a Identify and model plane figures, including collinear and non-collinear points, lines, segments, rays, and angles using appropriate mathematical symbols

Pearson: 1.2, 1.4IXL:LTF:

(Quality Core) D.1.bIdentify vertical, adjacent, complimentary, and supplementary angle pairs and use them to solve problems (e.g., solve equations, use proofs)

Pearson: 1.4, 1.5IXL:LTF:

(Quality Core) D.1.eLocate, describe, and draw a locus in a plane or space

Pearson: 1.2IXL:LTF:

(Quality Core) D.1.fApply properties and theorems of parallel and perpendicular lines to solve problems.(Quality Core) G.1.b Apply the midpoint and distance formulas to points and segments to find midpoints, distances, and missing information.


(Quality Core) F.1.aFind the perimeter and area of common plane figures, including triangles,


quadrilaterals, regular polygons, and irregular figures, from given information using appropriate units of measurement. (Quality Core) F.1.b Manipulate perimeter and area formulas to solve problems (e.g., find missing length)




First 9-weeksUnit 2: Reasoning and Proof 11 daysA primary resource for this Unit will be Pearson Geometry, in particular sections 2.2-2.6, though regular Geometry should consider reinforcing the concepts on patterns and inductive reasoning from section 2.1. ALCOS #9. Prove theorems about lines and angles. Theorems include vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; and points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. [G-CO9]

Pearson: 2.6IXL: C.1,2,3,4,8LTF: Logical Reasoning (This lesson gives students the opportunity to assign a true or false value to each of 10 “tricky” statements.)

(Prepares for) ALCOS #10. Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180º, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, and the medians of a triangle meet at a point. [G-CO10]

Pearson: 2.2-2.6IXL:LTF:

(Prepares for) ALCOS #11. Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [G-CO11]


(Quality Core) C.1.a. Use definitions, basic postulates, and theorems about points, segments, lines, angles, and planes to write proofs and to solve

Pearson: 2.2-2.6IXL: C.8

problems LTF:(Quality Core) C.1.b. Use inductive reasoning to make conjectures and deductive reasoning to arrive at valid conclusions


(Quality Core) C.1.c. Identify and write conditional and biconditional statements along with the converse, inverse, and contrapositive of a conditional statement; use these statements to form conclusions

Pearson: 2.2-2.4IXL: I.1,2,5,7,8

(Prepares for) (Quality Core) C.1.d. Use various methods to prove that two lines are parallel or perpendicular (e.g., using coordinates, angle measures)


(Quality Core) C.1.e. Read and write different types and formats of proofs including two-column, flowchart, paragraph, and indirect proofs





First 9-weeksUnit 3: Parallel and Perpendicular Lines 15 daysThe first part of this unit deals with angles formed by lines and a transversal, then extension is made to parallel lines cut by a transversal, and finally the Triangle-Angle Sum Theorem. The second part of the unit is devoted to parallel and perpendicular lines, both from a construction and an algebraic standpoint. The primary text resource here is Pearson Geometry (3.1-3.8).ALCOS #1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [G-CO1]

Pearson: 3.4IXL: D.1LTF:


Pearson: 3.6IXL: D.2,5LTF:

ALCOS #41. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3]


ALCOS #10. Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180º, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, and the medians of a triangle meet at a point. [G-CO10]

Pearson: 3.5IXL: D.3,4; F.2,3LTF:

ALCOS #31. Prove the slope criteria for parallel and Pearson: 3.7-3.8

perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [G-GPE5]

IXL: E.2 thru 6LTF: Tangent Line Equations (Teacher would need to briefly explain the equation of a circle, but this lesson does a good job driving home an important situation where we need a line perpendicular to a given line through a given point.)

(Quality Core) G.1.aUse slope to distinguish between and write equations for parallel and perpendicular lines.

Pearson: 3.7

(Quality Core) D.1.cIdentify corresponding, same-side interior, same-side exterior, alternate interior, alternate exterior angle pairs formed by a pair of parallel lines and a transversal and use these special angle pairs to solve problems (e.g., solve equations, use in proofs)

Pearson: 3.1-3.4

(Quality Core) C.1.d. Use various methods to prove that two lines are parallel or perpendicular (e.g., using coordinates, angle measures)

Pearson: 3.4,3.8IXL: E.3,4,6,7LTF:



Unit 4 - Second 9-weeks



Second 9-weeksUnit 4: Congruent Triangles 16 daysThe first part of this chapter provides the basics for ways triangles can be proven to be congruent, while the second section provides methods specific to certain triangle types (isosceles, equilateral, right, overlapping). The primary text resource for this unit is Pearson Geometry 4.1-4.6 for all levels, and Honors Geometry also visiting concepts in section 4.7.ALCOS #18. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. [G-SRT5]

Pearson: 4.1-4.7IXL: J.1 thru 3LTF:

ALCOS #10. Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180º, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, and the medians of a triangle meet at a point. [G-CO10]

Pearson: 4.5IXL: K.8,9LTF:

ALCOS #8. Explain how the criteria for triangle congruence, angle-side-angle (ASA), side-angle-side (SAS), and side-side-side (SSS), follow from the definition of congruence in terms of rigid motions. [G-CO8]

Pearson: 4.1-4.3IXL: K.1 thru 6LTF:


Pearson: 4.1-4.7IXL: K.2,4,6,7,9LTF:

(Quality Core) C.1.f. Prove that two triangles are congruent by applying the SSS, SAS, ASA, AAS, and HL congruence statements

Pearson: 4.1-4.3,4.6IXL: K.10LTF:

(Quality Core) C.1.g. Use the principle that corresponding parts of congruent triangles are congruent to solve problems

Pearson: 4.4IXL: K.7LTF:

(Quality Core) D.2.aIdentify and classify triangles by their sides and angle(Quality Core) D.2.jApply the Isosceles Triangle Theorem and its converse to triangles to solve mathematical and real-world problems


(Quality Core) E.1.bIdentify congruent figures and their corresponding parts


Unit 5 - Second 9-weeks



Second 9-weeksUnit 5: Relationships Within Triangles 12 daysThe main portion of this unit deals with concurrent lines in triangles, and the second part, which mostly pertains to Honors Geometry deals with indirect proof and inequalities in triangles. The main text resource for this unit is Pearson Geometry (5.1-5.4, 5.6 for Regular and 5.1-5.7 for Honors).ALCOS #10. Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180º, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, and the medians of a triangle meet at a point. [G-CO10]

Pearson: 5.1-5.4IXL: M.1 thru 4LTF:

ALCOS #18. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. [G-SRT5]

Pearson: 5.1-5.4IXL: M.5LTF:

ALCOS #9. Prove theorems about lines and angles. Theorems include vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; and points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. [G-CO9]

Pearson: 5.2IXL: B.6LTF:


Pearson: 5.1-5.4IXL: M.6LTF:

ALCOS #26. Construct the inscribed and Pearson: 5.2-5.3

circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. [G-C3]

IXL: M.6; U.16LTF:

** Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [A-CED]** Alg I Objectives – Review.


(Quality Core) D.2.bIdentify medians, altitudes, perpendicular bisectors, and angle bisectors of triangles and use their properties to solve problems (e.g., find points of concurrency, segment lengths, or angle measures)


(Quality Core) D.2.cApply the Triangle Inequality Theorem to determine if a triangle exists and the order of sides and angles


Unit 6a - Second 9-weeks



Second 9-weeksUnit 6a: Polygons and Quadrilaterals 10 daysThe first part of this unit is devoted to the general polygon-angle sum theorem, then emphasis is given to the various types of special quadrilaterals. The primary text resource is Pearson Geometry 6.1-6.6.ALCOS #11. Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [G-CO11]

Pearson: 6.2-6.6IXL: G.1 thru 4; N.1,2,4,5,6,7LTF: Handshake Problem (goes alongside the idea of counting total diagonals – connecting two points instead of connecting two people)

(Quality Core) C.1.i. Use properties of special quadrilaterals in a proof

Pearson: 6.2-6.6IXL: N.3,9,10LTF:

(Quality Core) D.2.gIdentify and classify quadrilateral, including parallelograms, rectangles, rhombi, squares, kites, trapezoids, and isosceles trapezoids, using their properties.


(Quality Core) D.2.hIdentify and classify regular and non-regular polygons (e.g., pentagons, hexagons, heptagons, octagons, nonagons, decagons, dodecagons) based on the number of sides given angle measures, and to solve real-world problems

(Quality Core) D.2.iApply the Angle Sum Theorem for triangles and polygons to find interior and exterior angle measures given the number of sides, to find the number sides given angle measures, and to solve real-world problems.


Unit 6b - Third 9-weeks



Third 9-weeksUnit 6b: Polygons and Quadrilaterals 5 daysThis unit (or sub-unit) deals with analytic geometry, or coordinate geometry, where specific coordinates are used to verify criteria, and general coordinates are used to prove theorems. The primary text resource is Pearson Geometry (6.7 for Regular Geometry, and 6.7-6.9 for Honors Geometry).ALCOS #11. Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [G-CO11]

Pearson: 6.7IXL: A.4; B.8LTF:



ALCOS #30. Use coordinates to prove simple geometric theorems algebraically. [G-GPE4] Example: Prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0,2)

Pearson: 6.7IXL:LTF: Coordinate Geometry and Proofs (This problem is really just about using variable coordinates to verify properties of a geometric figure on the coordinate plane.)

(Quality Core) C.1.i. Use properties of special quadrilaterals in a proof

Pearson: 6.7-6.9IXL:N.3,9,10LTF:

Unit 7 - Third 9-weeks



Third 9-weeksUnit 7: Similarity 10 daysSimilar polygons are the focus! This means we will use a lot of ratios to solve problems. The primary text resource is Pearson Geometry (7.1-7.5). Honors Geometry may consider whether 7.1 is helpful for your class, depending on the readiness of your students. ALCOS #18. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. [G-SRT5]

Pearson: 7.1-7.5IXL: A.1, P.1-7,11LTF:

(Algebra Standard for Review) Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [A-CED1]


ALCOS #17. Prove theorems about triangles. Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity. [G-SRT4]

Pearson: 7.5IXL: P.10LTF:

(Quality Core) C.1.h. Use several methods, including AA, SAS, and SSS, to prove that two triangles are similar, corresponding sides are proportional, and corresponding angles are congruent

Pearson: 7.3IXL: M.8LTF: Similar Triangles (This lesson explores the relationship between perimeters and areas of similar triangles.)

(Quality Core) D.2.dSolve problems involving the relationships formed when the altitude to the hypotenuse of a right triangle is drawn. (Quality Core) E.1.gDetermine the geometric mean between two numbers and use it to solve problems (e.g., find the lengths of segments in right triangles)


(Quality Core) E.1.cIdentify similar figures and use ratios and proportions to solve mathematical and real-world problems (e.g., finding the height of a tree using the shadow of the tree and the height and shadow of a person.

Person: 7.3IXL:LTF:

(Quality Core) E.1.dUse the definition of similarity to establish the congruence of angles, proportionality of sides, and scale factor of two similar polygons.


Unit 8 - Third 9-weeks



Third 9-weeksUnit 8: Right Triangles and Trigonometry 12 daysThis unit has some very important concepts for students moving on to more advanced math courses. These concepts include: Pythagorean Theorem, Converse of the Pythagorean Theorem, Special Right Triangles, Basic Triangle Trigonometry, and for Honors – Law of Sines and Law of Cosines. The primary text resource will be Pearson Geometry 8.1-8.4 for Regular Geometry and 8.1-8.6 for Honors.ALCOS #17. Prove theorems about triangles. Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity. [G-SRT4]

Pearson: 8.1IXL: Q.1,2LTF: Pythagorean Theorem Applications (More involved problems combining algebra and the Pythagorean Theorem); Introduction to Related Rates – Pythagorean Theorem (Good for writing equations for one side in terms of another side.)

ALCOS #19. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle leading to definitions of trigonometric ratios for acute angles. [G-SRT6]

Pearson: 8.2-8.4IXL: Q.4; R.1,3,5 thru 10LTF: Special Right Triangle Applications (Lots of topics in the applications – so it might be better near the end of the year.); Trig. Ratios with Special Right Triangles (Explores trig. function values for angles in special right triangles.)

ALCOS #20. Explain and use the relationship between the sine and cosine of complementary angles. [G-SRT7]

Pearson: 8.3-8.4IXL: R.4LTF:

ALCOS #21. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* [G-SRT8]

Pearson: 8.4IXL: R.10LTF: Vectors (Good word problems dealing with vectors. You could also share this with a Precalculus teacher.)


Pearson: 8.5IXL: R.10LTF:

(Honors Only) ALCOS #22. (+) Prove the Law of Sines and the Law of Cosines and use them to solve problems. [G-SRT10]

Pearson: 8.5-8.6IXL: R.11 thru 13LTF: Proof of Law of Sines (Guides students through the proof of law of sines.)

(Honors Only) ALCOS #23. (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). [G-SRT11]

Pearson: 8.5-8.6IXL: R.11 thru 13LTF:

(Quality Core) D.2.eApply the Pythagorean Theorem and its converse to triangles to solve mathematical and real-world problems (e.g., shadows, poles, and ladders)

(Quality Core) D.2.fIdentify and use Pythagorean triples in right triangles to find lengths of the unknown side


(Quality Core) H.1.aApply properties of 45-45-90 and 30-60-90 triangles to determine lengths of sides of triangles


(Quality Core) H.1.bFind the sine, cosine, and tangent ratios of acute angles given the side lengths of right triangles


(Quality Core) H.1.cUse trigonometric ratios to find the sides or angles of right triangles and to solve real-world problems (e.g., use angles of elevation and depression to find missing measures)

Pearson: 8.3-8.4 IXL:LTF:

Unit 10a - Third 9-weeks



Third 9-weeksUnit 10a: Area 10 daysIn this unit, we have several methods for finding areas of quadrilaterals and triangles, and we use trigonometry to find the area of a regular polygon. Then we move on to finding arc length and sector areas for circles. Finally, we apply all of these concepts to calculate geometric probability. The primary text for this unit is Pearson Geometry 10.1-10.7 for Regular Geometry, and 10.8 for Honors.ALCOS #33. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* [G-GPE7]

Pearson: 10.1-10.5IXL: S.1-6,8,11LTF: Areas of Triangles (Many methods for finding areas of triangles. Even if you don’t do all of them, students usually enjoy the variety of methods here.)


Pearson: 10.1-10.5IXL: S.8LTF:



ALCOS #13. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. [G-CO13]

Pearson: 10.3,10.5IXL:LTF:

ALCOS #34. Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. (Alabama only)

Pearson: 10.3,10.5IXL:LTF: Accumulation (Good review and/or application of area concepts to approximate the area of an irregular region under a curve.)

(Quality Core) G.1.cUse coordinate geometry to solve problems about geometric figures (e.g., segments, triangles,


quadrilaterals)

Unit 10b - Fourth 9-weeks



Fourth 9-weeksUnit 10b: Area 5 days


Pearson: 10.8IXL: S.12LTF:





ALCOS #13. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. [G-CO13]

Pearson: 10.7-10.8IXL: U.13,14,15LTF:

ALCOS #1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [G-CO1]

Pearson: 10.6IXL: S.7LTF:

ALCOS #24. Prove that all circles are similar. [G-C1] Pearson: 10.6-10.7IXL: P.9LTF:

ALCOS #28. Derive, using similarity, the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. [G-C5]

Pearson: 10.6-10.7IXL: S.7; U.3,4LTF:

(Honors Only) ALCOS 42. (+) Use probabilities to Pearson: 10.8

make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6]

IXL: S.8 thru 12; X.7LTF: Geometric Probability (Good review of some of the geometric probability concepts.)

(Honors Only) ALCOS #43. (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7]


(Quality Core) D.3.bDetermine the measure of central and inscribed angles and their intercepted arcs(Quality Core) F.1.dFind arc lengths and circumference of circles from given information (e.g., radius, diameters, coordinates)


(Quality Core) F.1.cUse area to solve problems involving geometric probability


(Quality Core) F.1.eFind area of a circle and the area of a sector of a circle from given information (e.g., radius, diameter, coordinates)


Unit 12 - Fourth 9-weeks



Fourth 9-weeksUnit 12: Circles 12 daysThis unit deals with the interaction of tangent lines and secant lines with circles. We will find angle measures in several situations, as well as segment lengths in those situations. Finally, we will work with equations of circles in the coordinate plane, and we will discuss what is meant by a “locus” of points. The primary text resource will be Pearson Geometry 12.1-12.6.ALCOS #25. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. [G-C2]

Pearson Geometry: 12.1-12.4IXL: U.1 thru 11LTF:

ALCOS #29. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. [G-GPE1]

Pearson Geometry: 12.5IXL: V.1 thru 5LTF:

(Honors Only) ALCOS #27. (+) Construct a tangent line from a point outside a given circle to the circle. [G-C4]

Pearson Geometry: 12.1IXL: U.12LTF: Tangent Line Equations (Good review of equations of perpendicular lines through a given point. Also a good application of tangent lines to coordinate geometry.)

(Quality Core) D.3.aIdentify and define line segments associated with circles (e.g., radii, diameters, chords, secants, tangents)

(Quality Core) D.3.cFind segment lengths, angle measures, and intercepted arc measures formed by chords, secants, and tangents intersecting inside and outside circles


(Quality Core) D.3.bDetermine the measure of central and inscribed angles and their intercepted arcs


(Quality Core) D.3.dSolve problems using inscribed and circumscribed polygons


(Quality Core) G.1.dWrite equations for circles in standard form and solve problems using equations and graphs





Fourth 9-weeksUnit 11: Surface Area and Volumes 16 days

This unit deals with cross-sections, surface areas, volumes, and ratios of these quantities between similar solids. The primary text resource is Pearson Geometry, 11.1-11.7 for both Regular and Honors, but a particular emphasis should be on 11.7 for the Honors course.ALCOS #38. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. [G-GMD4]

Pearson Geometry: 11.1-11.6IXL: H.1 thru 5LTF: Volumes of Revolution (Good chance for students to be exposed to revolutions where they can easily find the surface areas and volumes. You might not do this entire lesson, or you might want to!)


Pearson Geometry: 11.1-11.7IXL: T.1LTF:

ALCOS #35. Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. [G-GMD1]

Pearson Geometry: 11.6-11.7IXL: T.1LTF: Volume of a Sphere by Cross-Sections (This lesson uses the volume of a cylinder and the volume of a cone to derive the volume of a sphere using Cavalieri’s principle.)

ALCOS #36. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [G-GMD3]

Pearson Geometry: 11.2-11.7IXL: T.2 thru 6LTF:

ALCOS #40. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, British Thermal Units (BTUs) per cubic foot).* [G-MG2]

Pearson Geometry: 11.2-11.7IXL: T.1,9LTF:

ALCOS #37. Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama)

Pearson Geometry: 11.7IXL: T.7,8,9LTF:

(Quality Core) D.4.aIdentify and classify prisms, pyramids, cylinders, cones, and spheres and use their properties to solve problems

(Quality Core) F.2.aFind the lateral area, surface area, and volume of prisms, cylinders, cones, and pyramids in mathematical and real-world settings


(Quality Core) D.4.bDescribe and draw cross sections of prisms, cylinders, pyramids, and cones

(Quality Core) F.2.bUse cross sections of prisms, cylinders, pyramids, and cones to solve volume problems

Pearson: 11.1IXL:LTF

(Quality Core) E.1.fApply relationships between perimeters of similar figures, areas of similar figures, and volumes of similar figures, in terms of scale factor, to solve mathematical and real-world problems

(Quality Core) E.1.hIdentify and give properties of congruent or similar solids


(Quality Core) F.2.cFind the surface area and volume of a sphere in mathematical and real-world settings





Fourth 9-weeksUnit 9: Transformations 7 daysThis unit is an algebraic/coordinate approach to many of the Geometry concepts. It emphasizes the more algebraic definition of congruence (rigid motion), and distinguishes between which types of transformations lead to congruence, and which types lead to similarity. ALCOS #2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). [G-CO2]

Pearson Geometry: 9.1-9.7IXL: L.1-L.15LTF:

ALCOS #4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. [G-CO4]

Pearson Geometry: 9.1-9.7IXL: L.6LTF:

ALCOS #5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. [G-CO5]

Pearson Geometry: 9.1-9.7IXL: L.1,4,7,10LTF:

ALCOS #6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. [G-CO6]

Pearson Geometry: 9.1-9.7IXL: L.11LTF: Reflection of Lines (Good development of learning to reflect 2 points from a line instead of trying to reflect the whole line at once.)

ALCOS #3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. [G-CO3]

Pearson Geometry: 9.1-9.7IXL: L.11LTF:

ALCOS #7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. [G-CO7]

Pearson Geometry: 9.1-9.7IXL:LTF:

ALCOS #8. Explain how the criteria for triangle congruence, angle-side-angle (ASA), side-angle-side (SAS), and side-side-side (SSS), follow from the definition of congruence in terms of rigid motions. [G-CO8]


(Quality Core) C.1.f - Prove that two triangles are congruent by applying the SSS, SAS, ASA, AAS, and HL congruence statements


ALCOS #14. Verify experimentally the properties of dilations given by a center and a scale factor. [G-SRT1]a. A dilation takes a line not passing through the center of the dilation to a parallel line and leaves a line passing through the center unchanged. [G-SRT1a]b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. [G-SRT1b]


ALCOS #15. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. [G-SRT2]

Pearson Geometry: 9.1-9.7 IXL:LTF:

ALCOS #16. Use the properties of similarity transformations to establish the angle-angle (AA) criterion for two triangles to be similar. [G-SRT3]

Pearson Geometry: 9.1-9.7 IXL:LTF:

(Quality Core) E.1.aDetermine points or lines of symmetry and apply properties of symmetry to figures


(Quality Core) E.1.eIdentify and draw images of transformations and use their properties to solve problems

(Quality Core) G.1.eDetermine the effect of reflections, rotations, and translations, and dilations and their compositions on the coordinate plane


Alabama Technology Standards Ninth – Twelfth Grade

Operations and Concepts

Students will:

2. Diagnose hardware and software problems. Examples: viruses, error messages Applying strategies to correct malfunctioning hardware and software Performing routine hardware maintenance Describing the importance of antivirus and security software

3. Demonstrate advanced technology skills, including compressing, converting, importing, exporting, and backing up files. Transferring data among applications Demonstrating digital file transfer Examples: attaching, uploading, downloading

4. Utilize advanced features of word processing software, including outlining, tracking changes, hyperlinking, and mail merging.

5. Utilize advanced features of spreadsheet software, including creating charts and graphs, sorting and filtering data, creating formulas, and applying functions.

6. Utilize advanced features of multimedia software, including image, video, and audio editing.

Digital Citizenship

9. Practice ethical and legal use of technology systems and digital content. Explaining consequences of illegal and unethical use of technology systems and digital content Examples: cyberbullying, plagiarism Interpreting copyright laws and policies with regard to ownership and use of digital

content Citing sources of digital content using a style manual Examples: Modern Language Association (MLA), American Psychological Association (APA)

Research and Information Fluency

11. Critique digital content for validity, accuracy, bias, currency, and relevance.

Communication and Collaboration

12. Use digital tools to publish curriculum-related content. Examples: Web page authoring software, coding software, wikis, blogs, podcasts

13. Demonstrate collaborative skills using curriculum-related content in digital environments.

Examples: completing assignments online; interacting with experts and peers in a structured, online learning environment

Critical Thinking, Problem Solving, and Decision Making

14. Use digital tools to defend solutions to authentic problems. Example: disaggregating data electronically

Creativity and Innovation

15. Create a product that integrates information from multiple software applications. Example: pasting spreadsheet-generated charts into a presentation

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