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Question

In the given figure, AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD. Show that angle A > angle C and angle B > angle D
1047269_1af8d60f22d84699a9e61a21c9a4c921.png

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Solution

Construction Join A & C
Given
AB smallest
CD longest
InΔADC,CD>AD[CDislongest]DAC>DAC(i)[anglesoppositesideisgreater]InΔABC,BC>AB[ABissmallest]BAC>ACB(ii)[anglesoppositesideisgreater]Adding(i)&(ii),wegetDAC+BAC>DCA+ACBA>CHenceproved.(ii)ToproveB>DInΔABD,AD>AB[ABissmallest]ABO>AOB(i)[anglesoppositetosideisgreater]InΔBDC,CD>BCDBC>BDC(ii)Adding(i)&(ii),wegetABD+DBC>ADB+BDCB>Dhenceproved.

1219180_1047269_ans_6e04ca9c903a44e0ac14a158eb79e362.JPG

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