Question

Construct the diagonal of a square of side 5 cm using angle bisector construction method. What is the angle made by the diagonal with a side of the square?[3 MARKS]

Answer 1

Steps : 1 Mark
Construction : 2 Marks

Step:
1. Using set square construct square ABCD of side 5 cm. Each angle of square is ${90}^{\circ }$
2. Draw an arc of any radius with B as centre. Let the arc intersect AB and BC at E and G respectively.
3.Taking E and G as centres, draw arcs with radius more than $\frac{1}{2}EG$. Let both the arcs intersect at F
4. Join BF. Angle FBC is ${45}^{\circ }$. Extend $BF$ till it reaches D. $BD$ is a diagonal. It makes an angle ${45}^{\circ }$ with a side of the square.