Question
Construct a parallelogram $\text{ABCD}.$ Given:$AB = 3.5\ cm, AC = 4\ cm$ and $BD = 5.2\ cm$
✓
Answer
$AB = 3.5\ cm, AC = 4\ cm$ and $BD = 5.2\ cm$
Steps of construction:
$1)$ Since diagonals of a parallelogram bisect each other; construct $\triangle \text{OBC}$, such that:
$OB =\frac{1}{2} BD =\frac{1}{2} \times 5.2 \ cm =2.6 \ cm$
$OC =\frac{1}{2} AC =\frac{1}{2} \times 4 \ cm =2 \ cm $
And $A B=3.5 \ cm$.
$2)$ Produce $A O$ up to $C$, such that $A O=O C=2 \ cm$
$3)$ Join $B C, A D$ and $C D$.
$4) \text{ABCD}$ is the required parallelogram.
Steps of construction:
$1)$ Since diagonals of a parallelogram bisect each other; construct $\triangle \text{OBC}$, such that:
$OB =\frac{1}{2} BD =\frac{1}{2} \times 5.2 \ cm =2.6 \ cm$
$OC =\frac{1}{2} AC =\frac{1}{2} \times 4 \ cm =2 \ cm $
And $A B=3.5 \ cm$.
$2)$ Produce $A O$ up to $C$, such that $A O=O C=2 \ cm$
$3)$ Join $B C, A D$ and $C D$.
$4) \text{ABCD}$ is the required parallelogram.
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