Maths-

General

Easy

Question

# Prove in the given figure, side QR of a is produced to a point S.

If the bisector of and meet at the point T, then prove

Hint:

### Find ∠TQR and ∠TRS in terms of ∠PQR and ∠PRS respectively .

Now find the relation between ∠QPR ,∠PQR and ∠PRS also relation between ∠QTR ,∠TQR and ∠TRS. Now equate both the relations.

## The correct answer is: Hence proved

### ∠TQR = ∠PQR (TQ is the angular bisector )

∠TRS = ∠PRS (TR is the angular bisector )

We know that in a triangle, the exterior angle is always equal to the sum of the interior opposite angles.

In PQR ; ∠QPR +∠PQR = ∠PRS ∠QPR = ∠PRS -∠PQR — Eq1

In TQR ; ∠QTR +∠TQR = ∠TRS — Eq2

Substitute ∠TQR = ∠PQR and ∠TRS = ∠ PRS in Eq2

We get ∠QTR + ∠PQR = ∠PRS

∠QTR = ∠PRS - ∠ PQR

∠QTR = (∠PRS-∠PQR)

Substitute Eq1 in the above equation

We get ∠QTR = ∠QPR

Hence proved

Substitute Eq1 in the above equation

Hence proved

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