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AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD .show that angle a>angle c and angle b > angle d

Posted by Shaik Javeed 4 years, 9 months ago

CBSE > Class 09 > Mathematics

3 answers

Mansi Class12 4 years, 9 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

1Thank You

Rudransh Mishra 4 years, 9 months ago

Just draw diagonal and use theoram 7.8

0Thank You

Satyam Prajapati 4 years, 9 months ago

I do this question its so easy

0Thank You

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Posted by T Prudhvi 1 week, 5 days ago

CBSE > Class 09 > Mathematics