Question

Construct a triangle PQR in which Q = 45 degree , QR = 6 cm and PQ - PR = 4 cm​

Answer 1

1) Draw the base QR = 6 cm.

At point Q draw a ray QX making an ∠ QXR = 60o.

Here, PR-PQ = 4 cm

PR > PQ

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

2) Cut the line segment QS equal to PR-PQ = 4 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.