Construct Δ XYZ, in which YZ= 7.4cm, ∠XYZ = 45° and XY-XZ= 2.7cm

Given: Base YZ= 7.4cm, XY-XZ= 2.7cm and

∠Y = 45° of Δ XYZ.

Required: To construct a triangle XYZ.

Steps of construction:

i: Draw a segment YZ of length 7.4cm.

ii: Draw ray YL such that ∠Y = 45°

iii: Mark an arc on ray YL cutting at D such that YD = 2.7cm.

iv: Draw segment ZD.

v: Construct the perpendicular bisector of segment ZD.

vi: Name the point of intersection of ray YL and the perpendicular bisector of ZD as X.

vii: Draw segment XZ.

ΔXYZ is the required triangle.