Question

Using ruler and compasses only, draw a parallelogram whose diagonals are $4cm$ and $6cm$ long and contain an angle of ${75}^o$. Measure and write down the length of one of the shorter sides of the parallelogram.

Answer 1

Steps of construction:
(i) Draw a line segment $AC=6cm$
(ii) Bisect $AC$ at $O$.
(iii) At $O$, draw a ray $XY$ making an angle of ${75}^o$ at $O$.
(iv) From $OX$ and $OY$, cut off $OD=OB=4/2=2cm$
(v) Join $AB,BC,CD$ and $DA$
Thus, $ABCD$ is the required parallelogram.
On measuring one of the shorter sides, we get
$AB=CD=3cm$