# Construct the following and give justification :A triangle PQR given that QR = 3cm, $\angle PQR=45^{\circ}$ and QP – PR = 2 cm.

Given : QR = 3cm, $\angle PQR=45^{\circ}$ , QP – PR = 2 cm.

Steps of Construction :

1.         Draw line QR = 3 cm

2.         Draw line QB with $45^{\circ}$ angle at Q.

3.         Make an arc on QB of 2cm radius intersecting at A

4.         Join AR

5.         Bisect AR and extend it so it intersects QB at P

6.         Join PR

PQR is the required triangle.

Justification:

P lies on perpendicular bisector of AB.

Hence, PA = PQ

QA = PQ – PA

QA = PQ – PR           $\left (\because PA = PR \right )$

B

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