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9-12 Geometry Unit 1 Lesson 21

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K-5 Math 6-8 Math •9-12 Math

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

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Modeling Prompts

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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 21

One Hundred Eighty

Geometry

Practice

Problem 1

Student Task Statement

The triangles here are each obtained by applying rigid motions to Triangle 1.

<p>21 congruent triangle.</p>

Which triangles are translations of Triangle 1? Explain how you know.
Which triangles are not translations of Triangle 1? Explain how you know.

to access Practice Problem Solutions.

Problem 2

Student Task Statement

The quadrilateral is a parallelogram. Find the measure of angles 1, 2, and 3.

<p>A parallelogram with angle markings. Angle 1 in top left, Angle 2 in top right, 80 degrees in bottom left, and Angle 3 in bottom right.</p>

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Problem 3

ForLesson 20: Transformations, Transversals, and Proof

Student Task Statement

In the figure shown, lines and are parallel. Select the angle that is congruent to Angle 1.

<p>Parallel lines f and g cut by a transversal, creating angles 1, 2, 3 and 4 at intersection of lines g and transversal, and creating angles 5, 6, 7 and 8 at intersection of lines f and transversal.</p>

Angle 2
Angle 6
Angle 7
Angle 8

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Problem 4

ForLesson 20: Transformations, Transversals, and Proof

Student Task Statement

Angle is congruent to angle . Name another pair of congruent angles. Explain how you know.

<p>Triangle and two horizontal line segments.</p>

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Problem 5

ForLesson 20: Transformations, Transversals, and Proof

Student Task Statement

Describe a transformation that could be used to show that corresponding angles are congruent.
Describe a transformation that could be used to show that alternate interior angles are congruent.

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Problem 6

ForLesson 19: Evidence, Angles, and Proof

Student Task Statement

Lines and meet at point .

Which of these must be true? Select all that apply.

<p>Lines AD and EC intersect at point B.</p>

A 180-degree clockwise rotation using center takes to .

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Problem 7

ForLesson 19: Evidence, Angles, and Proof

Student Task Statement

Points , , and are collinear. Explain why points , , and are collinear.

<p>Lines AD and EC intersect at point B. Angles ABE and CBD are 30 degrees.</p>

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Problem 8

ForLesson 18: Practicing Point-by-Point Transformations

Student Task Statement

Draw the image of figure after a clockwise rotation around point using angle and then a translation by the directed line segment .
Describe another sequence of transformations that will result in the same image.

<p>A figure formed by 3 line segments, looks like the letter U. 4 points on the endpoints of the segments. Starting at the top left, A. Moving downard, C. Moving to the right, T. Moving upward, S.</p>

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Problem 9

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 ABC and A’B’C’.</p>

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Lesson 21 Resources

Student Materials

The image of after a 180-degree rotation using center lies on ray .

If a 180-degree rotation using center takes to , then it also takes to .

Angle is congruent to angle .

Angle is congruent to angle .