Question

In figure if PQ // RS, is ∆PQR - ∆SOQ, name the similarity.​

Answer 1

AAA similarity criteria is the name.

Consider the attached image while going through the following steps:

Given:  PQ ║ RS

To prove: ∆PQR - ∆SOQ

Proof: In ∆PQR and ∆SOQ

∠ POQ = ∠ SOR  (Vertically opposite angles)

∠ P = ∠ S (Alternate angles - given PQ ║ RS)

∠ Q = ∠ R (Alternate angles - given PQ ║ RS)

Therefore, using AAA similarity criteria,

we have proved that, ∆PQR - ∆SOQ

Answer 2

AAA similarly criterion:

∠P = ∠S & ∠Q = ∠R [alternate interior angles]

∠O = ∠O' [vertically opposite angles]