Navigation

9-12 Geometry Unit 1 Lesson 21

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

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

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

Lesson | Practice | Loading...

Sign in to access protected content and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

Curriculum

IM K-5 Math
IM 6-8 Math
IM 9-12 Math

Professional Learning

Illustrative Mathematics® has operated as an independent 501(c)3 non-profit organization since 2013.

©2024 Illustrative Mathematics®. Licensed under CC BY-NC 4.0.

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written permission of Illustrative Mathematics.

This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses. See the image attribution section for more information.

Settings

Audience

Not all roles available for this page.

Assessment Access

Sign in to view assessments and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

teacher
student
family

Unit 1, Lesson 21

One Hundred Eighty

Geometry

Practice

Problem 1

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

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>

to access Practice Problem Solutions.

Problem 3

ForLesson 20: Transformations, Transversals, and Proof

In the figure shown, lines \(f\) and \(g\) 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

to access Practice Problem Solutions.

Problem 4

ForLesson 20: Transformations, Transversals, and Proof

Angle \(BDE\) is congruent to angle \(BAC\). Name another pair of congruent angles. Explain how you know.

<p>Triangle and two horizontal line segments.</p> — \(\angle BDE \cong \angle BAC\)

to access Practice Problem Solutions.

Problem 5

ForLesson 20: Transformations, Transversals, and Proof

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.

to access Practice Problem Solutions.

Problem 6

ForLesson 19: Evidence, Angles, and Proof

Lines \(AD\) and \(EC\) meet at point \(B\).

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 \(B\) takes \(D\) to \(A\).
The image of \(D\) after a 180-degree rotation using center \(B\) lies on ray \(BA\).
If a 180-degree rotation using center \(B\) takes \(C\) to \(E\), then it also takes \(E\) to \(C\).
Angle \(ABC\) is congruent to angle \(DBE\).
Angle \(ABE\) is congruent to angle \(ABC\).

to access Practice Problem Solutions.

Problem 7

ForLesson 19: Evidence, Angles, and Proof

Points \(E\), \(B\), and \(C\) are collinear. Explain why points \(A\), \(B\), and \(D\) are collinear.

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

to access Practice Problem Solutions.

Problem 8

ForLesson 18: Practicing Point-by-Point Transformations

Draw the image of figure \(ACTS\) after a clockwise rotation around point \(C\) using angle \(CTS\) and then a translation by the directed line segment \(CT\).
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>

to access Practice Problem Solutions.

Problem 9

ForLesson 17: Working with Rigid Transformations

Triangle \(ABC\) is congruent to triangle \(A’B’C’\). Describe a sequence of rigid motions that takes \(A\) to \(A’\), \(B\) to \(B’\), and \(C\) to \(C’\).

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

to access Practice Problem Solutions.

Lesson 21 Resources

Student Materials