Construct Δ PQR, in which QR = 6.5cm, ∠PQR = 60° and PQ-PR = 2.5cm

Given: Base QR = 6.5cm,

PQ-PR = 2.5cm and

∠Q = 60° of Δ PQR.

Required: To construct a triangle PQR.

Steps of construction:

i: Draw a segment QR of length 6.5cm.

ii: Draw ray QL such that ∠Q = 60°

iii: Mark an arc on opposite ray QL i.e. QS cutting at D such that QD = 2.5cm.

iv: Draw segment RD.

v: Construct the perpendicular bisector of segment RD.

vi: Name the point of intersection of ray QL and the perpendicular bisector of RD as P.

vii: Draw segment PR.

ΔPQR is the required triangle.