Question

Construct a quadrilateral $ABCD$ in which $\overline{AB}=\overline{BC}=\overline{CD}=\overline{AD}=5$ cm and diagonal $\overline{AC}=6.5$ cm.

Answer 1

Draw a line segment $\overline{AB}=5cm$

Take $A$ as center with radius $6.5cm$ and draw an arc.

Take $B$ as center with radius $5cm$ and draw an arc, which cut off previous arc at point $C$

Take $A$ as center with radius $5cm$ and draw an arc.

Take $C$ as center with radius $5cm$ and draw an arc, which cut off Now, join $\overline{BC},\overline{CD},\overline{DA}$ and $\overline{AC}$

$\therefore$ $ABCD$ is required quadrilateral.