In given figure, PS, bisector of ∠P intersects side QR at point S. S

1.	In given figure, PS, bisector of ∠P intersects side QR at point S. SN ⊥ PQ and SM ⊥ PQ are drawn. Prove that SN = SM.
Answer» Given : In ∆PQS, PS is bisector of ∠P and SN ⊥ PQ and SM ⊥ PR. To Prove : SN = SM Proof : In ∆PSN and ∆PSM PS = PS (Common) ∠PNS = ∠PMS (Each 90° because SN ⊥ PQ and SM ⊥ PR) ∠NPS = ∠MPS (Since PS, bisector of ∠P) by A.A.S. congruence rule ∆ASP ≅ ∆PSM ∴ SN = SM Corresponding sides of congruent angles are equal.

In given figure, PS, bisector of ∠P intersects side QR at point S. SN ⊥ PQ and SM ⊥ PQ are drawn. Prove that SN = SM.

Answer»

Given : In ∆PQS, PS is bisector of ∠P and SN ⊥ PQ and SM ⊥ PR.

To Prove : SN = SM

Proof : In ∆PSN and ∆PSM

PS = PS (Common)

∠PNS = ∠PMS (Each 90° because SN ⊥ PQ and SM ⊥ PR)

∠NPS = ∠MPS (Since PS, bisector of ∠P)

by A.A.S. congruence rule

∆ASP ≅ ∆PSM

∴ SN = SM

Corresponding sides of congruent angles are equal.