Question

Explain how you would prove the triangles congruent in order to prove the statements true.

Answer 1

Given data:

QP = PT and RP = SP

Let us first prove ΔQPR and ΔSPT are congruent.

In ΔQPR and ΔSPT,

QP ≅ TP (Given side)

∠QPR ≅ ∠ SPT (Vertically opposite angles are congruent)

RP ≅ SP (Given side)

Therefore, ΔQPR ≅ ΔSPT (by SAS congruence rule)

By corresponding parts of congruence triangles are congruence,

⇒ ∠Q ≅ ∠T

Hence ∠Q ≅ ∠T.