In a quadrilateral ABCD,AB is the …
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Posted by Surya Sekhar Jena 5 years, 3 months ago
- 2 answers
Gaurav Seth 5 years, 3 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
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Surya Sekhar Jena 5 years, 3 months ago
0Thank You