Construct Δ PQR, in which QR= 4.2cm, ∠Q = 40° and PQ+PR= 8.5cm

Given: base QR= 4.2cm, PQ+PR= 8.5cm and

∠Q = 40° of Δ PQR.

Required: To construct a ΔPQR

Steps of construction:

s

i: Draw a segment QR of length of 4.2cm.

ii: At vertex Q, construct ∠Q = 40° and produce a ray QB.

iii: Mark an arc on ray QB cutting at D such that QD = 8.5cm.

iv: Draw segment DR.

v: Construct the perpendicular bisector of segment DR.

vi: Name the point of intersection of ray QB and the perpendicular bisector of DR as P.

vii: Draw segment RP.

ΔPQR is the required triangle.