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