Question

construct PQR in which QR=6cm,Angle Q = 60⁰ and PR - PQ =2 cm.​

Answer 1

Given: 

In ∆PQR, QR= 6 cm, PR-PQ=2 cm & ∠Q= 60°

Steps of construction:

1. Draw the base QR=6 cm.

At Point Q draw a ray QX making an  ∠XQR=60°

Here , PR -PQ= 2cmPR>PQ

The side containing the base angle Q is less than third side.

 2. Cut the line segment QS equal to PR-PQ=2 cm , from the ray QX extended on  opposite side of base QR.

3. Join SR and draw its perpendicular bisector ray AB which intersect SR at M.

4. Let P be the intersection point of SX and perpendicular bisector AB. Then join PR.

Thus ∆PQR is the required Triangle.