Lesson | 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 2

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

Lesson 2

2.1 Warm-up 2.2 Activity 2.3 Activity Student Lesson Summary

Unit 2, Lesson 2

Congruent Parts, Part 2

Geometry

2.1

Warm-up

Math Talk: Which Are Congruent?

Each pair of figures is congruent. Decide whether each congruence statement is true or false.

<p>Triangles A B C and D E F.</p>

Triangle is congruent to triangle .

<p>Concave quadrilaterals Z P M J and Y B L X.</p>

Quadrilateral is congruent to quadrilateral .

<p>Triangles J K L and Q R S. Angles J L K and Q R S appear to be right angles.</p>

Triangle is congruent to triangle .

<p>Pentagons A B C D E and P Q R S T.</p>

Pentagon is congruent to pentagon .

Are You Ready for More?

2.2

Activity

Which Triangles Are Congruent?

Standards Alignment

Building On

8.G.2

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

View Full Standard

Addressing

G-CO.6

Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

View Full Standard

Building Toward

Here are 3 triangles.

<p>Triangles A C E, P Q R, and L M N. They each have 1 angle of 46 point 6 degrees. They each have 2 sides of lengths 4 point 3 and 5 point 9.</p>

Triangle is congruent to which triangle? Explain your reasoning.
Show a sequence of rigid motions that takes triangle to that triangle. Draw each step of the transformation.
Explain why there can’t be a rigid motion from triangle to the other triangle.

2.3

Activity

Are These Parts Congruent?

Standards Alignment

Building On

8.G.2

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

View Full Standard

Addressing

G-CO.6

Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

View Full Standard

Building Toward

<p>Triangles A B D and C D B. Point E located on side D B.</p>

<p>Two concave polygons, G F O N M and H I J K L. G, H, M, and L are collinear.</p>

Triangle is a rotation of triangle around point by . Is angle congruent to angle ? If so, explain your reasoning. If not, which angle is congruent to?
Polygon is a reflection and translation of polygon . Is segment congruent to segment ? If so, explain your reasoning. If not, which segment is congruent to?
Quadrilateral is a rotation of polygon . Is angle congruent to angle ? If so, explain your reasoning. If not, which angle is congruent to?

Are You Ready for More?

Student Lesson Summary

Naming congruent figures so it’s clear from the name which parts correspond makes it easier to check whether two figures are congruent and to use corresponding parts. In this image, segment appears to be congruent to segment . Also, segment appears to be congruent to segment . So, it makes more sense to conjecture that triangle is congruent to triangle than to conjecture triangle is congruent to triangle .

<p>Triangles E F D and A B C.</p>

If we are told quadrilateral is congruent to quadrilateral , without even looking at the figures we know:

Angle is congruent to angle .
Angle is congruent to angle .
Angle is congruent to angle .
Angle is congruent to angle .

Segments and are congruent.
Segments and are congruent.
Segments and are congruent.
Segments and are congruent.

Quadrilaterals and can be named in many different ways so that they still correspond—such as is congruent to , or is congruent to . But is congruent to means there are different corresponding parts. Note that quadrilateral refers to a different way of connecting the points than quadrilateral .

<p>3 quadrilaterals: M A T H, L O V E, and A T M H. In quadrilateral A T M H, sides T M and H A cross over each other.</p>

Glossary

None

Have feedback on the curriculum?

Help us improve by sharing suggestions or reporting issues.

Submit Feedback

Standards Alignment

Building On

Addressing

G-CO.6

Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

View Full Standard

Building Toward

G-CO.7

Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

View Full Standard

Are You Ready for More?

G-CO.7

Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

View Full Standard

G-CO.8

Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

View Full Standard

G-CO.7

Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

View Full Standard