Question

Q. AB and CD are respectively the smallest and longest sides of quadrilateral
ABCD. Show that ZA > <C and B > ZD​

Answer 1

First of all join the diagonals.

Now in ∆ ABC,

As AB<BC,

angle ACB < angle CAB ........... (1)

in triangle ACD, CD greater than AD

therefore angle C a D is greater than angle ACD

angle ACD smaller than angle C a D............(2)

adding 1 and 2,

angle ACB + angle ACD < angle CAB + angle CAD

angle C smaller than angle A.

do similarly with triangles ABC and triangle cbp to get angle B greater than angle D.

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