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.

Navigation

9-12 Geometry Unit 2 Lesson 4

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

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

Settings

Audience

family

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 2, Lesson 4

Congruent Triangles, Part 2

Geometry

Practice

Problem 1

Match each statement using only the information shown in the pairs of congruent triangles.

In the two triangles there are 3 pairs of congruent sides.
The 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle.
The 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle.

Two adjacent triangles, sharing no sides, with the same orientation. The bottom side of both triangles is unmarked. The left side of each triangle has one tick mark, the upward facing angles each have one tick mark, and the right side of the triangles each have 2 tick marks.
Two adjacent congruent angles. One side of each triangle overlaps. The angles facing upwards next to the overlapping side in each triangle have 1 tick mark, the angles facing down next to the overlapping side each have two tick marks. The third angle is unmarked.

Problem 2

Sketch the unique triangles that can be made with angle measures and and side length 3. How many unique triangles are there? How do you know you have sketched all possibilities?

Problem 3

What is the least amount of information that you need to construct a triangle congruent to this one?

<p>Triangle JKL.</p>

Problem 4

ForLesson 3: Congruent Triangles, Part 1

Triangle is congruent to triangle . So Mai knows that there is a sequence of rigid motions that takes to .

<p>Congruent triangles ABC and EFG.</p>

Select all true statements after the transformations:

Angle coincides with angle .

Problem 5

ForLesson 3: Congruent Triangles, Part 1

A rotation by angle using point as the center takes triangle onto triangle .

<p>Triangle CBA and CDE.</p>

Explain why the image of segment lines up with segment .
Explain why the image of coincides with .
Is triangle congruent to triangle ? Explain your reasoning.

Problem 6

ForLesson 2: Congruent Parts, Part 2

Line is a line of symmetry for figure . Clare says that is congruent to because sides and are corresponding.

<p>Line EF is a line of symmetry for figure ABECDF.</p>

Why is Clare's congruence statement incorrect?
Write a correct congruence statement for the quadrilaterals.

Problem 7

ForLesson 2: Congruent Parts, Part 2

Triangle is the image of triangle after a reflection across line . Select all statements that must be true.

<p>Triangle H E F is the image of triangle H G F.</p>

Triangle is congruent to triangle .

Problem 8

ForLesson 1: Congruent Parts, Part 1

When rectangle is reflected across line , the image is . How do you know that segment is congruent to segment ?

<p>Rectangle ABCD with line EF through lines AB and DC at midpoints E and F.</p>

A rectangle has 2 pairs of parallel sides.
Any 2 sides of a rectangle are congruent.
Corresponding parts of congruent figures are congruent.
Congruent parts of congruent figures are corresponding.

Problem 9

ForLesson 22: Now What Can You Build?

This design began from the construction of a regular hexagon. Describe a rigid motion that will take the figure onto itself.

<p>Hexagon with line segments.</p>

Angle coincides with angle .

Segment coincides with segment .

Segment coincides with segment .

Segment coincides with segment .

Triangle is congruent to triangle .

Angle is congruent to angle .

Angle is congruent to angle .

Segment is congruent to segment .

Segment is congruent to segment .