Question

Construct a $△$ ABC in which BC = 4.5 cm, $\angle B={45}^{\circ }$ and AB + AC = 8 cm. Write steps of construction.

Answer 1

(i)Steps of construction:

Step 1: Draw BC = 4.5 cm
Step 2: Draw $\angle$ CBX = 45${}^{\circ }$
Step 3: From ray BX, cut-off line segment BD equal to AB + AC, i.e. 8 cm.
Step 4: Join CD.
Step 5: Draw the perpendicular bisector of CD meeting BD at A.
Step 6: Join CA.
Thus, $△$ ABC is the required triangle.