12 Geometry

12.01 Geometrical diagrams

12.02 Measuring angles

12.03 Parallel lines and transversals

12.04 Triangles

12.05 Angles within triangles

12.06 Quadrilaterals

12.07 Transformations and congruence

12.08 Testing for triangle congruence

12.09 Using triangle congruence

12.10 Quadrilaterals built from triangles

Stage 4

12.09 Using triangle congruence

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$ Q R = S T$

A

$$PQ=TU$ P Q = T U$

B

$$QR=TU$ Q R = T U$

C

$$PQ=ST$ P Q = S T$

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

Outcomes

MA4-17MG

classifies, describes and uses the properties of triangles and quadrilaterals, and determines congruent triangles to find unknown side lengths and angles

What is Mathspace

About Mathspace