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  • ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC.

ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC.

Answers (1)

Given: ABCD is a quadrilateral in which AB = BC and AD = CD

To prove :-      \angleADB =\angleBDC

and \angleABD = \angleDBC

Proof : In \triangleABD and \triangleCBD

AB = CD                                 (Given)

BD = BD                                 (common)

AB = BC                                 (given)

\triangleABD \cong \triangleCBD                       (SSS congruency)

\angleABD = \angleCBD          (by CPCT)

And \angleADB = \angleBDC  (by CPCT)

Therefore, BD bisects both the angle ABC and ADC.

Hence proved

Posted by

infoexpert24

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