Construct ΔXYZ, in which YZ= 6cm, XY+XZ= 9cm and ∠Y = 50°

Given:

base YZ= 6cm,

XY+XZ= 9cm and

∠Y = 50°

Required: To construct a ΔXYZ

Steps of construction:

i: Draw a segment YZ of length of 6cm.

ii: At vertex Y, construct ∠Y = 50° and produce a ray YA.

iii: Mark an arc on ray YA cutting at D such that YD = 9cm.

iv: Draw segment ZD.

v: Construct the perpendicular bisector of segment ZD.

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

vii: Draw segment XZ.

ΔXYZ is the required triangle.