Question

Construct $∆$ XYZ, such that XY + YZ =10.3 cm, YZ = 4.9 cm, $\angle$XYZ = ${45}^{°}$ .

Answer 1

Steps of constructions:

(1) Draw seg YZ of length 4.9 cm.
(2) Draw ray YV such that ∠ZYA = 45°.
(3) Mark point W on ray YA such that YB = 10.3 cm
(4) Draw seg BZ.
(5) Construct the perpendicular bisector of seg BZ .
(6) Name the point of intersection of ray YA and the perpendicular bisector of BZ as X.
(7) Draw seg XZ.
Therefore, △XYZ is the required triangle.