4. AB and CD are respectively the smallest and
longest sides of a quadrilateral ABCD
(see Fig. 7.50). Show that <A> Z C and
<B>ZD.
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Given that :-
AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD.
Prove that :-
∠A > ∠C and ∠B > ∠D
Proof :-
In ∆ABC
AB < BC
➻ ∠2 < ∠1 ... i { side
➻ In ∆ACD = AD < CD
➻ ∠3 < ∠4 ... ii { side
eq 1 + eq 2
➻ ∠2 + ∠3 < ∠1 + ∠4
➻ ∠C < ∠A Proved.
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