Question

Question 1 In the given figure, PS is the bisector of ∠QPR of ΔPQR. Prove that .

Class 10 - Math - Triangles Page 152

Answer 1

Let us draw a line segment RT parallel to SP which intersects extended line segment QP at point T

Given that, PS is the angle bisector of ∠QPR.

∠QPS = ∠SPR … (1)

By construction, ∠SPR = ∠PRT (As PS || TR) … (2)

∠QPS = ∠QTR (As PS || TR) … (3)

Using these equations, we obtain

∠PRT = ∠QTR

∴ PT = PR

By construction

PS || TR