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In a quadrilateral ABCD,AB is the …

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In a quadrilateral ABCD,AB is the smallest side and CD is the largest side.show that angle A greater than angle C and angle B greater than angle D

Posted by Surya Sekhar Jena 6 years, 4 months ago

CBSE > Class 09 > Mathematics

2 answers

Surya Sekhar Jena 6 years, 4 months ago

Thank you very much

0Thank You

Gaurav Seth 6 years, 4 months ago

Given:
In quadrilateral ABCD, AB smallest & CD is longest sides.

To Prove: ∠A>∠C
& ∠B>∠D

Construction: Join AC.
Mark the angles as shown in the figure..

Proof:
In △ABC , AB is the shortest side.

BC > AB
∠2>∠4 …(i)
[Angle opposite to longer side is greater]

In △ADC , CD is the longest side

CD > AD
∠1>∠3 …(ii)
[Angle opposite to longer side is greater]

Adding (i) and (ii), we have

∠2+∠1>∠4+∠3
⇒∠A>∠C

Similarly, by joining BD, we can prove that
∠B>∠D

0Thank You

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CBSE > Class 09 > Mathematics