Question

(11) CD and AB are respectively the smallest and longest sides of a quadrilateral ABCD.
Show that angle C is greater than angle A as well as angle D is greater than angle B.​

Answer 1

Answer:

Let ABCD be a quadrilateral such that AB is it's smallest side and CD is it largest side.

Now join AC and BD 

In ΔABC ,we have BC>AB 

⇒∠8>∠3 ...(1) {∵ angle opposite to longer side is greater.}

Since CD is the longest side of quadrilateral ABCD

In ΔACD, we have CD>AD

⇒∠7>∠4 ...(2)

Adding (1) and(2) we get

∠8+∠7>∠3+∠4

⇒∠A>∠C

Now in ΔABD, we have AD>AB {∵AB is the shortest side}

⇒∠1>∠6 ...(3)

In ΔBCD,we have CD>BC

⇒∠2>∠5 ....(4)

Adding (3) and (4)

∠1+∠2>∠5+∠6

⇒∠B>∠D

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