Question

Name a pair of overlapping congruent triangles in each diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL.

Answer 1

ΔPTS≅ΔRTA by AAS axiom of congruency

Explanation:

Consider ΔPQA and ΔRQS

∠PQA=∠RQS (Vertically Opposite Angles)

∠QAP=∠QSR (Complementary of two equal angles, ∠RAT and∠PST)

Due to angle sum property of a triangle, we come to the conclusion that

∠APQ=∠SRQ

Consider ΔPTS and ΔRTA

TA=TS (Given)

∠RAT=∠PST(Given)

∠APQ=∠SRQ (Proved above)

Therefore, ΔPTS≅ΔRTA by AAS axiom of congruency.