Question

Without using set square or protractor, construct rhombus $ABCD$ with sides of length $4$ cm and diagonal $AC$ of length $5$ cm. Measure $\angle ABC$. Find the point $R$ on $AD$ such that $RB=RC$. Measure the length of $AR.$

Answer 1

(i) Construct $AB=4$ cm.
(ii) Taking $A$ as centre, construct an arc of radius $5$ cm and with $B$ as centre construct another arc of $4$ cm radius which intersect each other at the point $C$.
(iii) Now join $ACandBD.$
(iv) With $A$ and $C$ as centre, construct two arcs of 4 cm radius which intersect each other on $D$.
(v) Join $AD$ and $CD$.
Hence, $ABCD$ is the required rhombus and by measure $\angle ABC={78}^{\circ }$
(vi) Construct perpendicular bisector of $BC$ which intersects $AD$ at the point $R$.
By measuring the length of $AR=1.2$ cm.