Question

Construct a $\Delta$ ABC in which BC = 8 cm, $\angle B={45}^{\circ }$ and AB - AC = 3.5 cm.

Answer 1

Steps of construction:
Step 1: Draw a line segment BC = 8 cm and at point B, make an angle of ${45}^{\circ }$ by bisecting ${90}^{\circ }$, say $\angle XBC={45}^{\circ }$
Step 2: Mark the line segment BD = 3.5 cm (equal to AB - AC) on the ray BX.
Step 3: Join DC and draw the perpendicular bisector PQ of DC, let it intersect BX at point A.
Step 4: Join AC,
Step 5: $\Delta$ ABC is the required triangle.