5. Congruence and Triangles

5.01 Congruence transformations

5.02 Corresponding parts of congruent triangles

5.03 SSS and SAS congruence criteria

5.04 ASA and AAS congruence criteria

5.05 Right triangle congruence

5.06 Modeling with congruent triangles (M)

United States of America

Grades 9-12

5.04 ASA and AAS congruence criteria

Adaptive

Worksheet

Interactive practice questions

Consider the two triangles in the diagram below:

Which of the following statements about $\triangle GHI$△GHI and $\triangle LMN$△LMN is true?

$\triangle GHI$△GHI$\cong$≅$\triangle LMN$△LMN based on the SSS congruence theorem.

A

$\triangle GHI$△GHI$\cong$≅$\triangle LMN$△LMN based on the SAS congruence theorem.

B

$\triangle GHI$△GHI$\cong$≅$\triangle LMN$△LMN based on the AAS congruence theorem.

C

$\triangle GHI$△GHI$\cong$≅$\triangle LMN$△LMN based on the HL congruence theorem.

D

$\triangle GHI$△GHI and $\triangle LMN$△LMN are not congruent.

E

There is not enough information to determine whether $\triangle GHI$△GHI$\cong$≅$\triangle LMN$△LMN.

F

Easy

< 1min

Consider the two triangles in the diagram below:

Easy

< 1min

Consider the two triangles in the diagram below:

Easy

< 1min

Consider the two triangles in the diagram below:

Easy

< 1min

Outcomes

G.CO.B.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.

G.CO.B.8

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

G.CO.C.10

Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

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