Question

Using ruler and compasses only construct A rhombus $ABCD$ given that $AB=5cm,AC=6cm$ measure $\angle BAD$.

Answer 1

Steps of construction:
(i) Draw a line segment $AB=5cm$
(ii) With centre $A$ and radius $6cm$, with centre $B$ and radius $5cm$, draw arcs intersecting each other at $C$.
(iii) Join $AC$ and $BC$
(iv) With centre $A$ and $C$ and radius $5cm$, draw arc intersecting each other $5cm$, draw arcs intersecting each other at $D$
(v) Join $AD$ and $CD$.
Thus, $ABCD$ is a rhombus
On measuring, $\angle BAD={106}^o$.