Topics
6. Congruence & Triangles
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United States of AmericaVirginia
Geometry

6.04 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 AAS congruence theorem.

A

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

B

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

C

$\triangle GHI$△GHI$\cong$≅$\triangle LMN$△LMN based on the SAS 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
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Outcomes

G.TR.2

The student will, given information in the form of a figure or statement, prove and justify two triangles are congruent using direct and indirect proofs, and solve problems involving measured attributes of congruent triangles.

G.TR.2a

Use definitions, postulates, and theorems (including Side-Side-Side (SSS); Side-Angle-Side (SAS); Angle-Side-Angle (ASA); Angle-Angle-Side (AAS); and Hypotenuse-Leg (HL)) to prove and justify two triangles are congruent.

G.TR.2b

Use algebraic methods to prove that two triangles are congruent.

G.TR.2d

Given a triangle, use congruent segment, congruent angle, and/or perpendicular line constructions to create a congruent triangle (SSS, SAS, ASA, AAS, and HL).

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