high school geometry days 91-101

8/12/2019 High School Geometry Days 91-101

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STRUCTURED CURRICULUM LESSON PLAN

Day: 091 Subject: Geometry Grade Level: High School

Correlations (SG,CAS,CFS): 9B1

TAP:Perform arithmetic operations involving

integers, fractions, decimals, and percents, explicitly stated or within contextChoose and apply appropriate operational

procedures and problem-solving strategies toreal-world situations

Understand number systemsUnderstand geometric properties and relationships; apply geometric concepts and

formulasApply a variety of estimation strategies:

standard rounding, order of magnitude, front-ending, compatible numbers, andcompensation

Use variables, number sentences, andequations to represent solutions and solve

problemsAnalyze and interpret data presented in charts,graphs, tables, and other displays

Understand and apply principles of probability,central tendency and variability

Demonstrate understanding of measurement concepts and apply measurement skills

ISAT:Solve problems requiring computations

with whole numbers, fractions, decimals, ratios, percents, and proportionsUnderstand and apply geometric concepts and

relationshipsUse mathematical skills to estimate,

approximate, and predict outcomes and tojudge reasonableness of resultsIdentify, analyze, and solve problems using

equations, inequalities, functions, and their graphs

Understand and use methods of data collectionand analysis, including tables, charts, andcomparisons

Demonstrate an understanding of measurement concepts and skills

Unit Focus/Foci

Exploring Quadrilaterals

Instructional Focus/Foci

Exploring Kites

Materials

Copies of Exploring KitesProtractors

Rulers


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D

A

B

C

Educational Strategies/Instructional Procedures

Review the properties of an isosceles triangle.

Have students draw two isosceles triangles that have a common base (BD) and label theremaining vertices A and C. Ask students to name the figure (Answer: Kite)

Have the students:1. Measure the angles of each triangle.2. Draw AC.Have students prove as many facts as they can about ABCD.

Discuss their findings, which should include:

1. The diagonal AC is a line of symmetry.2. The opposite angles, ABC and ADC, are congruent.3. The diagonals AC and BD are perpendicular.Have the students complete Exploring Kites.

Integration with Core Subject(s)

LA: Understand explicit, factual information

Apply information presented in the text to a new or different situationUnderstand the meaning of words in context

SC: Apply scientific method to solve problems

Analyze and interpret maps, charts, graphs, and cartoonsSS: Distinguish fact from opinion and relevant from irrelevant information

Connection(s)

Enrichment:

Fine Arts:


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Home: Have parent sign homework sheet weekly.

Remediation: Teachers Half Dozen

Technology:

Assessment

Teacher observation

Homework

Assign appropriate problems from your text.

Teacher Notes

Answers to Exploring Kites:

1. mD = mB

2. B is a right angle

4. 335. False6. False7. True


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EXPLORING KITES

AB = AD, CD = BC

1. Which angles are equal?2. If A and C are supplementary, what can you

conclude about ABC?

3. How long is CD if AD = 4x + 3, BC = 6x + 3,and AB = 6x 7?

Answer questions 4-6 true or false:

4. The opposite sides of kites are parallel.5. Kites must be convex.

6. If the diagonals of a kite bisect each other, thenall four sides of the kite will be equal.

D

A

B

C


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TAP:

Understand and apply geometric concepts and relationships

ISAT:

Identify, describe, compare, and classify geometric figures

Unit Focus/Foci



Recognizing and Applying Sufficient Conditions for Quadrilaterals to be Parallelograms

Materials

Copies of Quadrilateral Worksheet 1


Have the students complete Example 1 given below and discuss the solution.

Example 1:

Given parallelogram WXRT, find each of the following:

a) mZWX

b) mWXZ

c) mWZY

d) WZe) ZY

f) WUg) ZU

h) ZXi) WY

Answers:a) 85 b) 60 c) 95 d) 7 e) 13

f) 6 g) 10 h) 20 i) 12

W 13 X 450

10

U 7 6 350 400

Z Y


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Revisit the theorems used to determine whether a quadrilateral is a parallelogram.

1. the opposite sides are parallel2. the opposite sides are congruent

3. the opposite angles are congruent4. the diagonals bisect each other

5. a pair of opposite sides are parallel and congruent

Have the students complete Examples 2 and 3 and review the solutions.

Determine the values ofxandythat makes each quadrilateral a parallelogram.

Example 2:x+3y

5y 20 Answer: (x = 6, y = 4)

2(x + y) - 2

Example 3: Make acute angle 60

600

3x+y Answer: (x = 33, y = 21)

2(x-3)

Have students work in pairs to complete the Quadrilateral Worksheet.


LA: Understand explicit, factual informationUnderstand the meaning of words in context

Apply information presented in the text to a new of different situationSC: Apply scientific method to solve problemsSS: Distinguish fact from opinion and relevant from irrelevant information

Connection(s)

Enrichment:From newspaper and magazines, have the students create a collage using picturesof products that are parallelograms.

Fine Arts: See Enrichment

Home: Have students list the objects found in their homes that are quadrilaterals.



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Technology: Have students explore quadrilaterals using a drawing program such as CabriGeometry or Geometers Sketchpad.

Assessment

Evaluate the Quadrilateral Worksheet using the Structured Curriculum Scoring Rubric.

Homework


Teacher Notes

What kind of symmetry does a parallelogram have? reflection? rotation?

Use the 180rotational symmetry to describe the properties of a parallelogram.

Answers to Quadrilateral Worksheet 1

1. F

2. F3. F4. T

5. F6. x = 4, y = 47. x = 15, y = 75

8. x = 479. Yes. If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram.


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Quadrilateral Worksheet 1

Answer each statement trueorfalse.

1. The adjacent sides of a parallelogram are always congruent.

2. The consecutive angles of a parallelogram are always congruent.

3. Only one pair of opposite sides of a paralleogram are congruent.

4. The diagonals of a parallelogram bisect each other.

5. The diagonals of a parallelogram are perpendicular to each other.

Find the values of xandythat make each quadrilateral a parallelogram.

6. 7.

8.

9. Is this a parallelogram? Explain.

10. Given:BC FE ABF DEC

Prove: FECB is a parallelogram

x+3y

20 5x

2x+2y

(2x+y)0 y0

(5x)0

(3x-7)

(2x+40)0

80

F E D

6 648

52

A B C


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TAP:Understand geometric properties and

relationships

ISAT:Identify, describe, compare, and classify

geometric figures

Unit Focus/Foci



Recognizing and Applying the Properties of Quadrilaterals

Materials

Ruler

ProtractorGraph paper

Copies of Exploring Quadrilaterals 3


Review the homework assignment and answer any questions.

Have students complete Exploring Quadrilaterals 3.

Discuss the activity with the students.



Understand the meaning of words in contextSC: Analyze and interpret data

SS: Read and interpret maps, charts, graphs, and cartoons

Connection(s)

Enrichment:

Fine Arts:


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Home: Have parent sign homework record weekly.


Technology: Examine various quadrilaterals using Geometers Sketchpad or Cabri Geometry.

Assessment

Teacher observation

Homework


Teacher Notes

Answers to Exploring Quadrilaterals:

1. parallelogram

2. trapezoid

3. rectangle

4. trapezoid

5. parallelogram

6. rhombus


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Plot the points for each quadrilateral; use the ruler and protractor to help determine in which

category each quadrilateral belongs. List all possibilities.

1.

(-1, 0) (-2, 3) (-2,-2) (-3, 1)

2.

(3, 3) (4, 4) (3, 2) (4, -1)

...

.

.

...


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3.

(-1, 1) (4, 1) (1, -4) (-1, -4)

4.

(2, 2) (-1, -1) (4, 2) (2, -1)

. . . .

. .. .


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5.

(-1, 3) (5,3) (-3, -1) (3, -1)

6.

(4, 3) (6, 0) (4,-3) (2, 0)

. .. .

. ..

.


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TAP:


ISAT:

Identify, describe, compare, and classify geometric figures

Unit Focus/Foci



Recognizing and Applying the Properties of a Trapezoid

Materials



Have the students complete the 5-Minute Quiz.

5-Minute Quiz:

I. Each figure is a parallelogram. Identify the type and explain your reasoning.1) 3)

2) 4)

Review last nights homework and answer students questions (10-15 minutes).

Review the properties of a trapezoid with the students.


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Review the parts of a trapezoid. Have the students discuss the line of symmetry.

base 1

leg median leg

base 2

bases - The parallel sideslegs - The non-parallel sides

median - The segment joining the midpoints of the legs

Define isosceles trapezoidas a trapezoid with congruent legs. Explain to the students that thereare properties of isosceles trapezoids that do not apply to trapezoids in general.

1. Both pairs of base angles are congruent.

2. The diagonals are congruent.3. The median is parallel to the bases, and its measure is one-half the sum of the

measures of the bases.

Ask students to explain how the theorems work.

Have students complete Quadrilateral Worksheet 4.

Review the problems the students didnt understand.



SC: Analyze and interpret data

Connection(s)

Enrichment: Have students prove that the median is parallel to each base and the sum of thebases.

Fine Arts:

Home: Have parent sign homework record weekly.


Technology: Have students use a drawing program such as Geometers Sketchpad or CapriGeometry to investigate the properties of a trapezoid.


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Assessment

Observe students' work and check for understanding.

Homework


Teacher Notes

Remind students to begin to study for the unit assessment.

Construct a square. A B

A) Through point A, construct a segment the same length as AB . Call the segment AC .B) Keeping the compass at the same setting, construct the length of AB on AC . Construct an

arc, place the point on B, and construct an arc intersecting the other. Label the point ofintersection D.

Draw CD and BD .

Answers to 5-Minute Quiz:

1. Rhombus2. Rectangle3. Kite4. Square

Answers to Worksheet 2:

1. AB and ED2. FC

3. AE and BD4. 88, 97

5. 7

6. 47.29

7. 57

16or 5.4375

8. 52.89. x+1

10. 91

49 25and .


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Given IsoscelesTrapezoid ABDE

1. Identify the bases.

2. Identify the median.3. Identify the legs.4. = AED 92 Find M EAB and M BDE

5. If AE BD , AE=(2x-3), and BD=(4x-17). Findx.6. If BDE x + 40, =ABD x3 , DEA = (2X-11) and =EAB x . Findx.

7. If AB cm= 4

3

4and ED cm= 6

1

8. Find FC.

8. If FC=38.4and AB=24. Find ED.

9. If AB=x-1 and ED=x+3. Find FC in terms ofx.10. If AB=3x-5, FC=x+7, and ED=3x. Find AB.

A B

F C

E D


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TAP:


ISAT:

Identify, describe, compare, and classify geometric figures.

Unit Focus/Foci



Recognizing and Applying the Properties of a Rectangle

Materials



Review last nights homework and answer any questions students may have.

Review the properties of parallelograms and rectangles with the students.

Have the students complete Quadrilateral Worksheet 3.

Stop students after about 20 minutes to check for their understanding of the assignment.



Understand the meaning of words in contextApply information presented in the text to a new or different situation

SC: Apply scientific method to solve problemsSS: Distinguish fact from opinion and relevant from irrelevant information


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Connection(s)

Enrichment: Write a report on Frank Lloyd Wright and the buildings he designed. Include

photographs or illustrations.

Fine Arts: See Enrichment and Home.

Home: Take a walking tour of a Frank Lloyd Wright Home.


Technology: Research the use of Rectangles in Architecture.

Assessment

Evaluate Quadrilateral Worksheet 3 using the Structured Curriculum Scoring Rubric.

Homework

Review for the quiz.

Teacher Notes

Prepare copies of Quadrilateral Quiz for Day 099.

Answers for Quadrilateral Worksheet 3:

1. 16

2. 6

3. -3

4,3

4. 135. Not a rectangle - GM EO and GE and MO are not parallel

6. Not a rectangle - GM is not perpendicular to MO7. Not a rectangle - GM is not perpendicular to MO


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Find the value of x that would make ABCD a rectangle.

1. AE x= 3 9 , CE x= +2 72. AC x BD x= + = 4 8 6 4,

3. AC x BD x= = +4 9 92 ,

4. = = +ABD 4x 3, DBC 3x 2

A B

D C

Graph the following sets of points and determine if GEOM is a rectangle. Explain your answer.

5. G(-4,-1) E(0,1) O(0,-4) M(-4,-4)

6. G(-1,3) E(2,2) O(3,-1) M(0,0)7. G(5,3) E(3,5) O(5,7) M(7,5)

Extra Credit:

Given: RT WP

SP WP

Prove: RSPT is a rectangle

R S

W T Q P

E


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TAP:Understand and apply geometric concepts and

relationships


geometric figures

Unit Focus/Foci



Recognizing and Applying the Properties of a Rectangle

Materials

Copies of Quadrilateral Quiz


Allow 10 minutes for student questions.

Have students complete the Quadrilateral Quiz.




SC: Apply scientific method to solve problems


Connection(s)

Enrichment: Have students draw the information signs they see on their way to school such as

Fine Arts: See Enrichment

Home: See Enrichment


Technology: Have students research the international signs and symbols on the Internet.


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Assessment

Evaluate the Quadrilateral Quiz using the Structured Curriculum Scoring Rubric.

Homework

Read the section on squares and rhombi.

Teacher Notes

Review class notes.

1. a. diagonals bisect each other b. opposite sides are congruent c. opposite angles are congruent

d. opposite sides are parallel e. consecutive angles are supplementary

2. a. diagonals bisect each other b. diagonals are congruent

c. opposite sides are congruent d. opposite sides are parallel e. consecutive angles are supplementary

f. all four angles are right angles3. 64. 30

5. 39

6. 114


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Quadrilateral Quiz

1) List the properties of a parallelogram.

a)b)c)

d)e)

2) List the properties of a rectangle.

a)b)c)

d)e)

Refer to parallelogram ABCD: A B

3) If AE = 6, find EC. E

4) If mABE = 30, find mEDC.

D C5) If AB = (3x - 9)cm and DC = (2x + 9) cm, find AB.

6) If mDAB = 3x, mADC = 2x-10, find mBCD.


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relationships


geometric figures

Unit Focus/Foci



Recognizing and Applying the Properties of Squares and Rhombi

Materials

Construction Activity

CompassStraightedge


Review the properties of a square and rhombus with the students.

1. The diagonals bisect each other.2. The diagonals are congruent (square only).3. The diagonals are perpendicular.

4. Each diagonal bisects a pair of opposite angles.

Place this example on the chalkboard to check for understanding.

Given WXYZ is a rhombus with WY = XZ, determine whether each statement is true or false.

Give a reason for your answer. X Y

1) MZ = MX

2) XZ WY M3) mXYM = mYXM

W Z

4) XZ WY

5) Is WXYZ a square?


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Answers:

1) True - The diagonals bisect each other.2) True The information as given in the problem.

3) True - If two sides of a triangle are

, the opposite angles are

.4) True - The diagonals of a rhombus are perpendicular to each other.

5) Yes - XWZ YZW. m W m 180 m W + = = = Z 90

Demonstrate how to construct a rhombus with a compass and straightedge.

Have students complete the Construction Activity.




SC: Apply scientific method to solve problemsSS: Distinguish fact from opinion and relevant from irrelevant information

Connection(s)

Enrichment: Have students create an 81

2by 11 inch pencil drawing using only quadrilaterals

and shading.

Fine Arts:See Enrichment.

Home: Have parents sign assignment sheet weekly.


Technology: Have students use a drawing program such as Cabri Geometry or Geometers

Sketchpad to explore the properties of squares and rectangles.

Assessment

Teacher observation

Homework

Write step-by-step instructions explaining how to construct a square. Keep in mind yourinstructions may be given to another student to follow.


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Teacher Notes

A rhombus is a kite either way you look at it.

A C

D

You can also show this is true since a rhombus is a _______

A square is a rectangle; its diagonals are the same length.

The angle bisecting property also follows from the fact that rhombi are kites.

Prepare copies of Quadrilateral Worksheet 3.

Since AB = BC and AD = DC AE = ECSimilarly, BE = ED

B

E


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Construction Activity

Using a compass and a straightedge, construct a rhombus in the space below.

1. Draw a segment. Label it AB . Set the compass to match the length of AB .Construct an arc.

2. Label a point on the arc C.3. Without changing the setting on the compass place it at Cand construct an arc.4. Using the same measurement, place the point on B. Construct an arc that intersects

arc C. Label the point of intersection D.5. Use your straightedge to draw BC , CD , and AD .

How do you know your construction is a rhombus?


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relationships


geometric figures

Unit Focus/Foci



Recognizing and Applying Properties of Rhombi and Squares

Materials



Have the students exchange homework papers and use the instructions to construct a square theyprepared for homework (allow 15-20 minutes).

Have students complete Quadrilateral Worksheet 3. Monitor their progress.




Connection(s)

Enrichment: Have students design an international information sign.

Fine Arts: See Enrichment.

Home:Have parent sign homework sheet weekly.


Technology: Have students use a drawing program such as Geometers Sketchpad or Cabri

Geometry to investigate the properties of a Rhombus.


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Assessment

Evaluate Quadrilateral Worksheet 3 using the Structured Curriculum Scoring Rubric.

Homework


Teacher Notes

Prepare copies of Quadrilateral Worksheet 5.

Answers to Worksheet 4:

1. 15

2. 43

3. 32

4. 125. Squares, definition, have 4 equal sides.

6. a. rhombusb. rhombus7. Answers will vary


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Given Rhombus MAST with diagonals MS and AT

Complete the following:

1. If MS = 30, find MR2. If =MAT 43o , find TAS3. If TRS = (3x - 6), find x.

4. If MT=(4x-18) and MA=(3x-6), find x.5. Explain why every square is a rhombus.

6. Determine whether the coordinates form a rhombus.

a. (-1,0) (1,-1) (2,1) (0,2)b. (-3,-3) (1,-6) (5,-3) (1,0)

7. Survey the classroom and list examples of a rhombus and a square.

M

A

R

T

S


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relationships


geometric figures

Unit Focus/Foci



Recognizing and Applying the Properties of Quadrilaterals

Materials

Copies of Drawing Quadrilaterals


Have the students complete Drawing Quadrilaterals.

Review last nights homework assignment and answer any questions.

Have the students complete the following 5-Minute Quiz.

Polygons

Place a check in the box if the property holds true for that polygon.

Properties Parallelogram Rectangle Rhombus Square Trapezoid

both pairopposite sides

opposite s

are

opposite s

are supplementary


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Understand the meaning of words in contextSC: Analyze and interpret data


Connection(s)

Enrichment: Have the students create a mobile of the quadrilaterals using recycled products.

Fine Arts: See Enrichment.

Home: Have parents sign student assignment sheet.


Technology:

Assessment

Evaluate the 5-Minute Quiz using the Structured Curriculum Scoring Rubric.

Homework

Study for Unit Assessment.

Prepare a list of review questions to be shared with the class.

Teacher Notes

Prepare Unit Six Assessment. Prepare copies of Vocabulary 6 Activity.


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Drawing Quadrilaterals

There are 16 different quadrilaterals that can be made on a 3x3 dot matrix. Drawas many as you can and name each one.

________ ________ _________ _________

________ ________ _________ _________

________ ________ _________ _________

________ ________ _________ _________


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relationships


geometric figures

Unit Focus/Foci



Recognizing and Applying the Properties of a Parallelogram.

Materials

Review Wheel

Copies of Vocabulary 6 Activity


Have the class complete Vocabulary 6 Activity.

Have the class play Review Wheel (from Appendix C).



SC: Analyze and interpret dataSS: Read and interpret maps, charts, graphs, and cartoons

Connection(s)

Enrichment: Have the students make an Equilateral Triangle from a paper circle.

Fine Arts:See Enrichment.

Home: See Enrichment.



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Technology:

Assessment

Teacher observation

Homework

Study for tomorrows exam.

Teacher Notes

Prepare Unit Six Assessment.

To make an equilateral triangle from a circle:

1. Mark the center of the circle.2. Fold from any point of the circle to the center.

3. Fold to the center from one end of the fold.4. Fold the remaining part.

.A B

.D

C


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Vocabulary 6 Activity

Across

1. quadrilateral with four right angles and four congruent sides4. segment that joins the midpoints of the legs of a trapezoid

6. a segment from a vertex of the triangle to the opposite side and perpendicular to the line

containing that side

8. quadrilateral with two distinct pairs of adjacent congruent sides

9. polygon where no line contains both a side of the polygon and a point in the interior of the

polygon

11. a statement accepted as true without any proof

16. quadrilateral with both pairs of opposite sides parallel18.polygon in which a diagonal lies in the exterior of the polygon, excluding the endponts19.convex polygon with all congruent sides and anglesDown

2. a four sided polygon3. a segment that joins a vertex of the triangle at the midpoint of the opposite side5. a segment joining nonconsecutive vertices in a polygon

7. quadrilateral with four right angles

10. quadrilateral with one pair of parallel sides

11. a closed figure formed by three or more coplanar segments

12. an angle that forms a linear pair with one of the angles of the polygon

13. having the same measure

14. quadrilateral with all four sides congruent

15. the side opposite the right angle in a right triangle

17. nonparallel sides of a trapezoid


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relationships


geometric figures

Unit Focus/Foci



Recognizing and Applying the Properties of a Parallelogram

Materials

Copies of Unit Six Assessment


Have students complete the Unit Six Assessment.





Connection(s)

Enrichment: Have the students write a paragraph explaining how to create a square from a

rectangular piece of paper without measuring.

Fine Arts:

Home: See Enrichment.


Technology:


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Assessment

Evaluate the Unit Six Assessment using the Structured Curriculum Scoring Rubric.

Homework

Have students select three pieces of their work for their portfolio and write an explanation as towhy each piece was selected.

Teacher Notes

To create a square from a rectangular piece of paper:

1. Fold one corner so that it meets the other side.2. Draw a straight line along the edge.3. Cut along the straight line.

4. Unfold the square.

Answers to Unit Six Assessment:

1. T

2. T3. F4. T5. T6. T7. F8. F9. F10.T11.Yes, the opposite sides are congruent12.Yes, the opposite sides are congruent13.x = 714.x = 5y + 215.x = 9


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UNIT SIX ASSESSMENT

Answer each of the questions true or false.

1. The diagonals of a square bisect each other.2. The diagonals of a rhombus are congruent.3. A trapezoid is a parallelogram.4. Every square is a rhombus.5. The opposite angles of a parallelogram are congruent.6. All angles of a rhombus are congruent.7. The median of a trapezoid is equal to the product of its bases.8. All quadrilaterals have at least one right angle.9. Consecutive angles of a rectangle are complementary.10.Every square is a rectangle.Determine whether the quadrilateral MATH with the given vertices is a parallelogram.Explain your answer.

11.M(2, 5), A(5, 9), T(3, -1), H(6, 3)

12.M(-2, 5), A(6, 5), T(6, -3), H(-2, -3)


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Find the value of x.

13. Given parallelogram HELP

HE = 4x 3 and LP = 18 + x

14. Given trapezoid ABCDAB = 4x + 6 and CD = 6x 2

15. Given rhombus RSTURT = 2x + 4 and SU = 3x - 5

R

UT

S

22

C D

BA

LP

H E

high school geometry days 91-101

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