Topics
6. Congruence & Triangles
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United States of AmericaVirginia
Geometry

6.05 Right triangle congruence

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

Consider the two triangles in the diagram below:

Two right triangles, $\triangle PQR$△PQR and $\triangle ABC$△ABC, have their vertices marked with solid dots. The triangle above is $\triangle PQR$△PQR, labeled with vertices $P$P, $Q$Q, $R$R. The $\angle PRQ$∠PRQ is marked with a yellow square, indicating a right angle. The hypotenuse, side $PQ$PQ measures $7$7 units and is opposite the right angle, $\angle PRQ$∠PRQ. The side $PR$PR is opposite $\angle PQR$∠PQR. The side $RQ$RQ is opposite $\angle RPQ$∠RPQ. The triangle below is $\triangle ABC$△ABC, labeled with vertices $A$A, $B$B, and $C$C. The $\angle BCA$∠BCA is marked with a small yellow square, indicating a right angle. The hypotenuse, side $BA$BA measures $7$7 units and is opposite the right angle, $\angle BCA$∠BCA. The side $CA$CA is opposite $\angle CBA$∠CBA. The side $BC$BC is opposite $\angle CAB$∠CAB. Both side $PR$PR of $\triangle PQR$△PQR and side $CA$CA of $\triangle ABC$△ABC measure $4$4 units.

Which of the following statements about $\triangle PQR$△PQR and $\triangle ABC$△ABC is true?

$\triangle PQR$△PQR$\cong$≅$\triangle ABC$△ABC based on the SSS congruence theorem.

A

$\triangle PQR$△PQR$\cong$≅$\triangle ABC$△ABC based on the SAS congruence theorem.

B

$\triangle PQR$△PQR$\cong$≅$\triangle ABC$△ABC based on the AAS congruence theorem.

C

$\triangle PQR$△PQR$\cong$≅$\triangle ABC$△ABC based on the HL congruence postulate.

D

$\triangle PQR$△PQR and $\triangle ABC$△ABC are not congruent.

E

There is not enough information to determine whether $\triangle PQR$△PQR$\cong$≅$\triangle ABC$△ABC.

F
Medium
< 1min

Consider the two triangles in the diagram below:

Medium
< 1min

In the diagram, $MQ$MQ is perpendicular to $PR$PR, and $\Delta MPR$ΔMPR is isosceles.

Medium
1min

In the diagram, $\overline{HJ}\parallel\overline{KL}$HJ∥KL and $\overline{HK}\cong\overline{LJ}$HK≅LJ.

Medium
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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