For triangles ABC and PQR, which of these sets of equal parts is NOT enough to prove that the two triangles are congruent?

AB = PQ

BC = QR

and

CA = RP

Correct answerYour answer

AB = PQ

\angle B = \angle Q

and

BC = QR

Correct answerYour answer

\angle A = \angle P

\angle B = \angle Q

and

\angle C = \angle R

Correct answerYour answer

\angle A = \angle P

\angle B = \angle Q

and

AB = PQ

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Three equal sides (SSS), two sides with the included angle (SAS), and two angles with a side (ASA or AAS) each prove congruence.
Three equal angles only fix the SHAPE, not the size: a small and a large equilateral triangle have the same angles.
So $\angle A = \angle P$ , $\angle B = \angle Q$ and $\angle C = \angle R$ is not enough.

Worth noting

AAA proves the triangles are similar, not congruent.

Ten questions from Lines, Triangles and Circles, at your own pace.

Explanation