Question

Using ruler and compasses only, construct rhombus $ABCD$ with sides of length $4cm$ and diagonal $AC$ of length$5cm$. Measure $\angle ABC$.

Answer 1

Steps of construction:
(i) Draw a line segment $AC=5cm$
(ii) With centre $A$ and $C$ and radius $4cm$, draw arcs intersecting each other above and below $AC$ at $D$ and $B$.
(iii) Join $AB,BC,CD$ and $DA.$
Thus, $ABCD$ is the required rhombus.