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9-12 Geometry Unit 1 Lesson 20

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

Algebra 1 •Geometry Algebra 2 Extra Support Materials for Algebra 1

Unit

•Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8

Modeling Prompts

Lesson

Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19 •Lesson 20 Lesson 21 Lesson 22

K-5
6-8
9-12

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Integrated Math 1
Integrated Math 2
Integrated Math 3

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8

Modeling Prompts

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14
Lesson 15
Lesson 16
Lesson 17
Lesson 18
Lesson 19
Lesson 20
Lesson 21
Lesson 22

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Unit 1, Lesson 20

Transformations, Transversals, and Proof

Geometry

Practice

Problem 1
Student Task Statement
Priya: “I bet if the alternate interior angles are congruent, then the lines will have to be parallel.”

Han: “Really? We know if the lines are parallel then the alternate interior angles are congruent, but I didn't know that it works both ways.”

Priya: “Well, I think so. What if angle and angle are both 40 degrees? If I draw a line perpendicular to line through point , I get this triangle. Angle would be 50 degrees because . And because the angles of a triangle sum to 180 degrees, angle is 90 degrees. It's also a right angle!”

Han: “Oh! Then line and line are both perpendicular to the same line. That's how we constructed parallel lines, by making them both perpendicular to the same line. So lines and must be parallel.”

Horizontal lines A I and G J. Line F E passes through line G J at point C and line A I at point B.

Label the diagram based on Priya and Han's conversation.

Is there something special about 40 degrees? Write a conjecture about a pair of alternate interior angles measuring degrees.

Prove your conjecture.

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Problem 2

ForLesson 19: Evidence, Angles, and Proof

Student Task Statement

What is the measure of angle ?

<p>Lines AD and EC intersect at point B. Angle CBD is 50 degrees.</p>

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Problem 3

ForLesson 19: Evidence, Angles, and Proof

Student Task Statement

Lines and are perpendicular. The dashed rays bisect angles and . Explain why the measure of angle is 45 degrees.

<p>Lines AB and BC are perpendicular and meet at point B. Dashed rays BF and BE bisect angles ABD and CBD.</p>

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Problem 4

ForLesson 18: Practicing Point-by-Point Transformations

Student Task Statement

Identify a figure that is not the image of quadrilateral after a sequence of rigid transformations. Explain how you know.

<p>6 quadrilaterals.</p>

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Problem 5

ForLesson 17: Working with Rigid Transformations

Student Task Statement

Quadrilateral is congruent to quadrilateral . Describe a sequence of rigid motions that takes to , to , to , and to .

<p>Two congruent quadrilaterals labeled ABCD and A’B’C’D’.</p>

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Problem 6

ForLesson 17: Working with Rigid Transformations

Student Task Statement

Triangle is congruent to triangle . Describe a sequence of rigid motions that takes to , to , and to .

<p>Two congruent triangles labeled A prime B prime C prime and ABC.</p>

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Problem 7

ForLesson 16: More Symmetry

Student Task Statement

Identify any angles of rotation that create symmetry.

<p>Flower on polar grid. Grid is made up of 3 circles with the same center. Flower is made up of 3 congruent petals, equally spaced. 2 petals on top half of grid, 1 petals on bottom. Petal length reaches the third outermost circle on the grid.</p>

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Problem 8

ForLesson 16: More Symmetry

Student Task Statement

Select all the angles of rotation that produce symmetry for this flower.

<p>Flower on polar grid.</p>

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Problem 9

ForLesson 14: Defining Rotations

Student Task Statement

Three line segments form the letter N. Rotate the letter N clockwise around the midpoint of segment by 180 degrees. Describe the result.

<p>The letter N, formed by 3 line segments. 4 points on the endpoints of the segments. Starting at the bottom left, A. Moving upward, B. Slanting down and to the right, C. Moving upward, D.</p>

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Lesson 20 Resources

Student Materials