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Name: _____________________________________________ Date: _______________________ Period: _________

Plane & Coordinate GeometryTopic: Line Segments & Distance Date:Main Ideas/Questions

Notes & Examples

Measuring

Segments

The distance between two points A and B is

written as _________________ or _______. AB = ________

Congruent

Segments

If _____________________, then the segments are congruent. This is written as

__________________.____________________ on the figure also

indicate congruence.

SegmentAdditionPostulate

If A, B, and C, are collinear points and B is between A and C, then

_______________________________________

Examples Example 1: Finding Measurements by Adding or SubtractingFind XZ. Assume that the figure is not drawn to scale.

You Try!A. Find the length of AB. B. Find the length of ON .

Example 2: Write and Solve Equations to Find MeasurementsFind the value of x and ST if T is between S and U, ST = 7x, SU = 45, and

TU = 5x-3

You Try!

If CE = 7x+4, find the value of X and DE.

Procter R Hug High School 1 Advanced Algebra 3 Plane & Coordinate Geometry

DistanceFormula

Used to find the distance between two points (x1, y1) and (x2, y2)

Formula:

ExamplesGraph the ordered pairs &

check by using the Pythagorean Theorem.

Example 3: Find Distance on a Coordinate PlaneFind the distance between E(-4, 1) and F(3, -1).

You Try!

Find the distance between A(-3, 4) and M(1,2).

Example 4: Find Distance Josh is standing at the 30-yard line, 15 yards from the sideline, when he throws the football. Johnny catches it on the other team’s 20-yard line, 5 yards from the same sideline. How far did Josh throw the ball?

Topic: Locating Points and Midpoints

Date:

Main NotesProcter R Hug High School 2 Advanced Algebra 3 Plane & Coordinate Geometry

Ideas/QuestionsMidpointFormulaOn Number

Line

Used to find the distance between two points x1 and x2

Formula:

Examples Real –World Example 1: Find the Midpoint on a Number LineDECORATING Marco places a couch so that its end is perpendicular and 2.5 feet away from the wall. The couch is 90” wide. How far is the midpoint of the couch back from the wall in feet?

You Try!

Use the number line to find the midpoint of AX.

MidpointFormula

in Coordinate Plane

Used to find the distance between two points (x1 , y1) and (x2, y2)Formula:

Examples

Find a Missing

End Point

Example 2: Find the Midpoint in the Coordinate PlaneFind the coordinates of M, the midpoint of GH , for G(8, -6) and H(-14, 12).

You Try!

Find the coordinates of the midpoint of XY for X(-2,3),and Y(-8,-9).

Example 3: Find Missing CoordinatesFind the coordinates of D if E(-6, 4) is the midpoint of DF and F has coordinates (-5, -3).


You Try!

Find the coordinates of R if N (8, –3) is the midpoint of RS and S has coordinates (–1, 5).

Example 4: Find Missing MeasuresWhat is the measure of PR if Q is the midpoint of PR.

You Try!

What is the measure of AC if B is the midpoint of AC.

Topic: Angle Measure Date:Main Ideas/Questions

Notes

Angles

An angle is formed by two __________ with a common endpoint. This common endpoint is called the ____________________ The rays are called the ___________________. Name an angle using __________ letters. The middle letter must


always represent the vertex! Use a single letter if there is only one angle located at the vertex. When referring to the measure of an angle, use a lowercase m.

Example: m∠ABC = 60°

Types of Angles

Interior Exterior

Congruent Angles

If _____________________________, then the angles are congruent. This is written as ________________________.

Angle Bisector

A ___________ that divides an angle into _________ _______________________ ____________________.

In the diagram to the right, _______________ is an angle

bisector, therefore, __________________________________.

Examples Real-World Example 1: Angle and Their PartsA. Name all angles that have B as a vertex.

B. Name the sides of ∠5.

C. Write another name for ∠6.

You Try!A. Which angle has point X as a vertex?

B. Which ray is a side of ∠3?

C. Which of the following is another name for ∠3?


Example 3: Find the Angle MeasureINTERIOR DESIGN Wall stickers of standard shapes are often use to provide a stimulating environment for a young child’s room. A five-pointed star sticker is shown with vertices labeled. Find m∠GBH and m∠HCI if ∠GBH≅ ∠HCI, m∠GBH=2x+5, and m∠HCI = 3x-10.

You Try!Find m∠BHC and m∠DJE if ∠BHC ≅ ∠DJE, m∠BHC = 4x + 5, and m∠DJE

= 3x + 30.

Topic: Angle Relationships Date:

Main Ideas/Questions

Notes


Perpendicular Lines

Two lines that ___________________ at a _______________ ________________.

The symbol for perpendicular is __________.In the diagram to the right, ___________________.

Perpendicular Bisector

A line, segment, or ray ________________________ to a segment at its ____________________.

In the diagram to the right, ________ is the perpendicular bisector to _________.

Examples Real-World Example 1: Identify Angle PairsA. ROADWAYS Name an angle pair that satisfies the condition two angles that form a linear pair.

B. Name an angle pair that satisfies the condition two acute vertical angles.

You Try!A. Name two adjacent angles whose sum is less than 90.

B. Name two acute vertical angles.

Example 2: Angle MeasureALGEBRA Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the measure of the other angle.

You Try!ALGEBRA Find the measures of two complementary angles if one angle measures six degrees less than five times the measure of the other.

Example 3: Perpendicular Lines


ALGEBRA Find x and y so that KOand ´HM are perpendicular.

You Try!ALGEBRA Find x so that ADand CE are perpendicular.

Topic: 1-6 Two-Dimensional Figures

Date: WU


Notes

Polygon A polygon is a _____________ figure formed by a _______________ number of coplanar segments, called sides.Name a polygon by the letters of the verticies, written in order of consecutive verticies.

Concave Convex

Equilateral Polygon Equiangular Polygon Regular Polygon

Examples# of sides

Polygon

3 Triangle4 Quadrilater

al5 Pentagon6 Hexagon7 Heptagon8 Octagon9 Nonagon10 Decagon11 Hendecago

n12 Dodecagonn n-gon

Example 1: Name and Classify PolygonsName the polygon by its number of sides. Then classify it as convex or concave and regular or irregular. A. B.

You Try!Name the polygon by the number of sides. Then classify it as convex or concave and regular or irregular.


Perimeter, Circumference,

& Area

p =

b = h =A =ℓ = w = C =r =d =

A. B.

Triangle Square Rectangle Circle

Example 2: Find Perimeter and AreaFind the perimeter or circumference and area of the figures.

You Try!Find the perimeter or circumference and area of the figures.

Example 3: Largest AreaTerri has 19 feet of tape to mark an area in the classroom where the students may read. Which of these shapes has a perimeter or circumference that would use most or all of the tape?


A. a square with side length of 5 feet

B. a circle with the radius of 3 feet

C. a right triangle with each leg length of 6 feet

D. a rectangle with a length of 8 feet and a width of 3 feet

You Try!Each of the following shapes has a perimeter of about 88 inches. Which one has the

greatest area?

A. a rectangle with a length of 26 inches and a width of 18 inches

B. a square with side length of 22 inches

C. a right triangle with each leg length of 26 inches

D. a circle with radius of 14 inches

Example 4: Perimeter and Area on the Coordinate PlaneCOORDINATE GEOMETRY Find the perimeter and area of pentagon ABCDE with A(0, 4), B(4, 0), C(3, −4), D(−3, −4), and E(−3, 1).

Step 1: Perimeter Step 2: Area


You Try!Find the perimeter of quadrilateral WXYZ with W(2, 4), X(–3, 3), Y(–1, 0), and Z(3, –1).

Topic: 1-7 Transformations in the Plane

Date: WU



Notes

Examples

Example 1: Identify Rigid TransformationsIdentify the type of rigid transformation shown as a reflection, translation, or rotation.

You Try!Identify the type of rigid transformation shown as a reflection, translation, or rotation.


Reflection_____________

over a line called the

______ _____

______________________Each point of the preimage

and its image are the

_______

____________________ from the line of reflection

Translation_____________

Moves all the points of the original figure the

_________

__________________

in the _________

__________________.

Rotation_____________

around a fixed point called

the __________ ____

_____________, through a

specific

__________________,

and in a specific

____________________.

Transformation

RulesReflection in the x-

axis(x, y) →

(x, -y)Reflection in the y-

axis(x, y) → (-

x, y)Reflection in the line

y=x(x, y) →

(y, x)Rotation of 90° CCW

about the origin

(x, y) → (-y, x)

Rotation of 180°

about the origin

(x, y) → (-x, -y)

Rotation of 270°

CCW about the

origin

(x, y) → (y, -x)

Translation by a vector

(x, y) → (x+a, y+b)

*Negatives mean to “change the sign”

Example 2: Identify a Real-World TransformationBRIDGES Refer to the picture to the left. Identify the type of rigid transformation shown by the image of the bridge in the river as a reflection, translation, or rotation.

You Try!GAME Identify the type of congruence transformation shown by the image of the chess piece as a reflection, translation, or rotation.

Example 3: Reflections on the Coordinate PlaneConsider △PSR that has coordinates P(−3, 4), S(−3, −1), and R(−6, 2). Determine the coordinates of the vertices of the image after a reflection in the x-axis.

You Try!Triangle ABC with vertices A(–1, –4), B(–4, –1), and C(–1, –1) is a transformation of ΔXYZ with vertices X(–1, 4), Y(–4, 1), and Z(–1, 1). Graph the original figure and its image. Identify the transformation and verify that it is a congruence transformation.


Example 4: Translations on the Coordinate PlaneFor parallelogram ABCD with vertices A(−2, 1), B(−1, 4), C(3, 1), and D(4, 4), find the coordinates of the vertices of the image after a translation along the vector ⟨−1,2 ⟩.

SCORE ___________

Topic: 1-8 Three-Dimensional Figures

Date: WU


Notes

Polyhedrons

A polyhedron is a solid with all __________________________ that enclose a single region of space.

Each flat surface or ______________________ is a polygon. The line segments where the faces ________________________ are

called __________. The point where three or more edges intersect is called a

_____________________.

Examples of Polyhedrons

Examples of Non-

Polyhedrons


Examples

Example 1: Identify SolidsIdentify the solid.

You Try!Identify the solids.

Surface Area and Volume

T =P = V =B =h =ℓ = r =

Prism Regular Pyramid

Cylinder Cone Sphere


Examples Example 2: Find Surface Area and VolumeFind the surface area and the volume of the cone.

You Try!Find the surface area and volume of the triangluar prism.

Real-World Example 3: Surface Area and VolumeCONTAINERS Mike is creating a mailing tube which can be used to mail posters and architectural plans. The diameter of the base is 3 34 inches,

and the height is 2 23 feet. Find the amount of cardboard Mike needs to make the tube, then find the volume of the tube.


You Try!Jenny has some boxes for shipping merchandise. Each box is in the shape of a rectangular prism with a length of 18 inches, a width of 14 inches, and a height of 10 inches. Find the surface area and volume of the box.


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