Question

Let ABCD be a quadrilateral in which AD is the largest side and BC is smallest side. Prove that ∠A < ∠C.(Hint: Join AC)

Answer 1

∠A < ∠C , ABCD is a quadrilateral in which AD is the largest side and BC is smallest side.

Step-by-step explanation:

ABCD is a quadrilateral in which AD is the largest side and BC is smallest side.

join AC

in Δ ABC

BC < AB   as BC is smallest side

=> ∠BAC < ∠BCA   (as sides are in the order of angle opposite to them)

in Δ ADC

CD < AD   as AD is largest side

=> ∠DAC < ∠DCA

Adding both

∠BAC + ∠DAC  < ∠BCA + ∠DCA

=> ∠BAD  < ∠BCD

=> ∠A < ∠C

QED

Proved

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