10. Congruence and Triangles

10.01 Congruence transformations

10.02 Corresponding parts of congruent triangles

10.03 SSS and SAS congruence criteria

10.04 ASA and AAS congruence criteria

10.05 Right triangle congruence

United States of America

Grades 9-12

10.02 Corresponding parts of congruent triangles

Adaptive

Worksheet

Interactive practice questions

Given that $\triangle PQR$△PQR$\cong$≅$\triangle STU$△STU:

Two triangles, $\triangle PQR$△PQR and$\triangle STU$△STU, have their vertices marked with solid dots. The triangle above is $\triangle PQR$△PQR, labeled with vertices $P$P, $Q$Q, and $R$R. The side $QR$QR is opposite $\angle QPR$∠QPR. The side $PQ$PQ is opposite $\angle PRQ$∠PRQ. The side $PR$PR is opposite $\angle PQR$∠PQR. The triangle below is $\triangle STU$△STU, labeled with vertices $S$S, $T$T, and $U$U. The side $TU$TU is opposite $\angle TSU$∠TSU. The side $ST$ST is opposite $\angle SUT$∠SUT. The side $US$US is opposite $\angle STU$∠STU. Both $\angle PRQ$∠PRQ of $\triangle PQR$△PQR and $\angle SUT$∠SUT of $\triangle STU$△STU are marked with a yellow-shaded single arc. Both $\angle QPR$∠QPR of $\triangle PQR$△PQR and $\angle TSU$∠TSU of $\triangle STU$△STU are marked with a blue-shaded double arc.

Which of the following statements are true?

$$\overline{QR}\cong\overline{ST}$QR≅ST$

A

$$\overline{PQ}\cong\overline{ST}$PQ≅ST$

B

$$\overline{QR}\cong\overline{TU}$QR≅TU$

C

$$\overline{PQ}\cong\overline{TU}$PQ≅TU$

D

Easy

< 1min

Given that $\triangle CDE$△CDE$\cong$≅$\triangle LMN$△LMN:

Easy

< 1min

Given that $\triangle GHI$△GHI$\cong$≅$\triangle LMN$△LMN:

Easy

< 1min

Given that $\triangle STU$△STU$\cong$≅$\triangle ABC$△ABC:

Easy

< 1min

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.

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