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7. Geometry
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Middle Years

7.04 Congruent triangle problems

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Interactive practice questions

It is known that $\triangle PQR\equiv\triangle STU$△PQR≡△STU.

Two triangles $\triangle PQR$△PQR and $\triangle STU$△STU are congruent. In triangle $\triangle PQR$△PQR, $\angle QPR$∠QPR at vertex $P$P is marked with a double arc and is shaded blue, and $\angle PRQ$∠PRQ at vertex $R$R is marked with a single arc and is shaded yellow. In triangle $\triangle STU$△STU, $\angle UST$∠UST at vertex $S$S is marked with a double arc and is shaded blue, and $\angle SUT$∠SUT at vertex $U$U is marked with a single arc and is shaded yellow. Angles $\angle QPR$∠QPR and $\angle UST$∠UST are congruent as indicated by their identical marks. Angles $\angle PRQ$∠PRQ and $\angle SUT$∠SUT are congruent as indicated by their identical marks. Side $QR$QR is opposite angle $\angle QPR$∠QPR. Side $PQ$PQ is opposite $\angle PRQ$∠PRQ. Side $UT$UT is opposite $\angle UST$∠UST. Side $ST$ST is opposite $\angle SUT$∠SUT. 

Which two of the following equalities do we know to be true?

$QR=ST$QR=ST

A

$PQ=TU$PQ=TU

B

$QR=TU$QR=TU

C

$PQ=ST$PQ=ST

D
Easy
< 1min

It is known that $\triangle CDE\equiv\triangle LMN$△CDE≡△LMN.

Easy
1min

It is known that $\triangle GHI\equiv\triangle LMN$△GHI≡△LMN.

Easy
< 1min

It is known that $\triangle STU\equiv\triangle ABC$△STU≡△ABC.

Easy
< 1min
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