In the adjoining figure, TR = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that RB = SA.

∠1 = ∠4 (Vertically opposite angles)

⇒ 2∠2 = 2∠3

⇒ ∠2 = ∠3.

TS = TR (Given)

⇒ ∠TRS = ∠TSR (As angle opposite to equal side are equal)

⇒ ∠TRS - ∠2 = ∠TSR - ∠3

⇒ ∠ARB = ∠BSA.

∠RTB = ∠STA (Common angle)

△RBT ≅ △SAT (By ASA axiom.)

We know that corresponding sides of congruent triangles are equal.

∴ RB = SA.

Hence, proved that RB = SA.