Question

RS PQ Complete the proof that PQR = RSP

Answer 1

Option D:

SAS

Solution:

Given $\overline{R S} \ || \ \overline{P Q}$

To prove that $\triangle P Q R \cong \triangle R S P$

In ΔPQR and ΔRSP,

$\overline{R S}\cong\overline{P Q}$ (given side)

$\overline{R S} \ || \ \overline{P Q}$ (given)

By alternative interior angle theorem,

∠PRS ≅ ∠QPR (angle)

By reflexive property of congruence,

$\overline{PR } \cong \overline{PR}$ (side)

Hence by Side-Angle-Side (SAS) congruence rule,

ΔPQR ≅ ΔRSP

Option D is the correct answer.

Hence the missing reason is SAS.