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

Step 1:

Draw a line QR=3cm.

Step 2:
Construct an angle of 45° at Q.

Step 3:

With Q as center and 2cm as radius cut an arc on QX at S.

Step 4:
Join SR and bisect it.

Name the intersecting point of QX and the bisector P.

Step 5:

Join PR.

PQR is the required Triangle.

Justification

QR and ∠PQR =45°.

P lies on the perpendicular bisector of SR.

PS = PR

Given,

QS = PQ – PS

= PQ -PR (as PS=PR)

Thus The construction is justified.