If the measure of sides of quadrilaterals are given as AB - 4cm- CD - 5 cm- and angles are given as -ABC-75- -BCD-45- and -CDA-135- Can you construct a unique quadrilateral ABCD- With measure of -DAB- Yes-Yes-No-With measure of BC- Yes-

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2 Adjacent Sides, 3 Angles

If the measur...

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?

Yes

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With measure of $∠$ DAB, Yes

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With measure of BC, Yes

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Solution

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.

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Similar questions

If the measure of sides of quadrilaterals are given as AB = 4 cm, 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?

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?

Q. The measurements of a quadrilateral are given as AB

= 4 c m

, CD

= 5 c m

∠

ABC

= 75^{\circ}

∠

BCD

= 45^{\circ}

and

∠

CDA

= 135^{\circ}

. Can you construct a unique quadrilateral ABCD?

Q. The measurements of a quadrilateral are given as

A B = 4 c m, C D = 5 c m, ∠ A B C = 75^{\circ}, ∠ B C D = 45^{\circ}

and

∠ C D A = 135^{\circ}

.
Can you constant a unique quadrilateral ABCD?

If the measure of the sides of a quadrilateral are given as AB = 4cm, CD = 5cm, and angles are given as ∠ ABC = $75^{\circ}$ , ∠ BCD = $35^{\circ}$ and ∠ CDA = $135^{\circ}$ , can you construct a quadrilateral ABCD?

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

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?