Question

If the measure of sides of quadrilaterals are given as AB = 4cm, CD = 5 cm, and angles are given as ∠ABC=${75}^{\circ }$, ∠BCD=${45}^{\circ }$ and ∠CDA=${135}^{\circ }$. Can you construct a unique quadrilateral ABCD?

• A. Yes
• B. No
• C. With measure of $\angle$DAB, Yes
• D. With measure of BC, Yes

Answer 1

The correct option is D

With measure of BC, Yes

We need atleast 5 measurements to construct a unique quadrilateral.

Measurements of 3 angles are given. If we have the measurements of 2 adjacent sides, construction will be possible.

But the lengths of the adjacent sides are not given.

So, if the measurement of either BC or AD is given, construction will be possible.

The correct answer is, yes if the measure of BC is known.