Topics
10. Congruence and Triangles
topic badge
United States of America
Grades 9-12

10.04 ASA and AAS congruence criteria

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

Consider the two triangles in the diagram below:

Two triangles, $\triangle GHI$△GHI and $\triangle LMN$△LMN, have their vertices marked with solid dots. The triangle above is $\triangle GHI$△GHI, labeled with vertices $G$G, $H$H, and $I$I. The $\angle IGH$∠IGH measures $28^\circ$28° and is marked with a yellow-shaded double arc. The $\angle GIH$∠GIH measures $63^\circ$63° and is marked with a red-shaded single arc. The side $IH$IH is opposite $\angle IGH$∠IGH. The side $GH$GH is opposite $\angle GIH$∠GIH. The side $GI$GI is opposite $\angle IHG$∠IHG. The triangle below is $\triangle LMN$△LMN, labeled with vertices $L$L, $M$M, and $N$N. The $\angle NLM$∠NLM measures $28^\circ$28° and is marked with a yellow-shaded double arc. The $\angle LNM$∠LNM measures $63^\circ$63° and is marked with a red-shaded single arc. The side $MN$MN is opposite $\angle NLM$∠NLM. The side $LM$LM is opposite $\angle LNM$∠LNM. The side $LN$LN is opposite $\angle LMN$∠LMN. The side $GH$GH of $\triangle GHI$△GHI and side $LM$LM of $\triangle LMN$△LMN are congruent, as indicated by single tick marks.

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
Sign up to access Practice Questions
Get full access to our content with a Mathspace account
Book a Demo
Sign up for free

Outcomes

HSG.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.

HSG.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.

HSG.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.

What is Mathspace

About Mathspace