Question

Using ruler and compasses only, construct the quadrilateral $ABCD$ in which $\angle BAD={45}^o$, $AD=AB=6cm,BC=3.6cm,CD=5cm.$Measure $\angle BCD.$

Answer 1

Steps of construction:
(i) Draw a line segment $AB=6cm$
(ii)At $A$, draw a ray $AX$ making an angle of ${45}^o$ and cut off $AD=6cm$
(iii)With centre $B$ and radius $3.6cm$ and with centre $D$ and radius $5cm$, draw two arcs intersecting each other at $C$.
(iv) Join $BC$ and $DC$.
Thus, $ABCD$ is the required quadrilateral.
On measuring $\angle BCD$, it is ${60}^o$