A triangle PQR given that QR = 3cm, ∠ PQR = 45° and QP – PR = 2 cm.

Question

Construct:

A triangle PQR given that QR = 3cm, ∠ PQR = 45° and QP – PR = 2 cm.

Answer 1

According to the question,

We have to draw a triangle PQR such that QR = 3cm, ∠ PQR = 45° and QP – PR = 2 cm

Steps of construction:

1. Draw a ray OX and cut off a line segment QR = 3 cm.

2. AT Q, construction ∠YQR = 45^o.

3. From QY, cut off QS = 2 cm.

4. Join RS.

5. Draw perpendicular bisector of RS to Meet QY at P.

6. Join PR. Then PQR is the required triangle.