Question

Construct $∆$ XYZ, such that YZ = 7.4 cm, $\angle$XYZ = ${45}^{°}$ and XY $-$ XZ = 2.7 cm.

Answer 1

Steps of construction:

(1) Draw seg YZ of length 7.4 cm.
(2) Draw ray YP such that ∠ZYP = 45°
(3) Take point Q on ray YP such that YQ = 2.7 cm.
(4) Construct the perpendicular bisector of seg QZ.
(5) Name the point of intersection of ray YP and the perpendicular bisector of seg QZ as X.
(6) Draw seg XZ.

Therefore, △XYZ is required triangle.