7. Congruence & Triangles

7.01 Congruent figures

7.02 SAS and SSS congruence criteria

7.03 ASA and AAS congruence criteria

7.04 Congruence in right triangles

7.05 Corresponding parts of congruent triangles

7.06 Medians and altitudes in triangles

7.07 Centers of triangles

7.08 Midsegments of triangles

United States of America Tennessee

Integrated Math 2

7.03 ASA and AAS congruence criteria

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

Outcomes

M2.G.CO.B.6

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.

M2.G.CO.B.7

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

M2.G.SRT.B.3

Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures.

M2.MP1

Make sense of problems and persevere in solving them.

M2.MP3

Construct viable arguments and critique the reasoning of others.

M2.MP5

Use appropriate tools strategically.

M2.MP6

Attend to precision.

M2.MP7

Look for and make use of structure.

M2.MP8

Look for and express regularity in repeated reasoning.

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