Option D:
SAS
Solution:
Given [tex]\overline{R S} \ || \ \overline{P Q}[/tex]
To prove that [tex]\triangle P Q R \cong \triangle R S P[/tex]
In ΔPQR and ΔRSP,
[tex]\overline{R S}\cong\overline{P Q}[/tex] (given side)
[tex]\overline{R S} \ || \ \overline{P Q}[/tex] (given)
By alternative interior angle theorem,
∠PRS ≅ ∠QPR (angle)
By reflexive property of congruence,
[tex]\overline{PR } \cong \overline{PR}[/tex] (side)
Hence by Side-Angle-Side (SAS) congruence rule,
ΔPQR ≅ ΔRSP
Option D is the correct answer.
Hence the missing reason is SAS.
