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  • AB and CD are the smallest and largest sides of a quadrilateral ABCD. Out of angle B and angle D decide which is greater

AB and CD are the smallest and largest sides of a quadrilateral ABCD. Out of \angleB and \angleD decide which is greater

Answers (1)

ABCD is quadrilateral

AB and CD are smallest and greatest side of ABCD.

Join BD

In \triangleBCD

DC < BC                                 (\because CD is Greatest side)

\angleCBD > \angleBDC          (Angle opposite to greater side is greater)                …(i)

In \triangleABD

AD > AB                                 (AB is the smallest side)

\angleABD > \angleADB         (Angle opposite to greater side is greater)                …(ii)

Adding (i) and (ii)

\angleCBD + \angleABD > \angleBDC + \angleADB

\angleABC >\angleADC

Hence \angleB is greater.

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infoexpert24

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