Question

Construct a parallelogram, ABCD with side BC = 4.5 cm, diagonal AC = 5.6 cm and diagonal BD = 5.0 cm. [4 MARKS]

Answer 1

Concept : 1 Mark
Steps : 1 Mark
Construction : 2 Marks

Concept :

Diagonals of a parallelogram bisect each other. i.e., $\text{OB = OD and OA = OC}$

Steps of construction :
1. Construct a $\Delta OBC$ such that
$OB=\frac{1}{2}BD=\frac{1}{2}\times 5cm=2.5cm$
$OC=\frac{1}{2}AC=\frac{1}{2}\times 5.6cm=2.8cm$
$BC=4.5cm$
2. Extend $BO$ upto $D$, such that $OD=OB=2.5cm$ and extend $CO$ upto $A$, such that $OA=OC=2.8cm$
3. Join AB, AD and CD
​4. ABCD is the requaired parallelogram.