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  • ABCD is a quadrilateral such that diagonal AC bisects the angles A and C. Prove that AB equal to AD and CB equal to CD.

ABCD is a quadrilateral such that diagonal AC bisects the angles A and C. Prove that AB = AD and CB = CD.

Answers (1)

Given: ABCD is quadrilateral

AC bisects \angleA and \angleC

To prove: AB = AD, CB = CD

In \triangleABC and \triangleADC

\angleBAC = \angleDAC                      (\because AC bisects \angleA)

AC = AC                                             (common)

\angleBAC = \angleDCA                      (\becauseAC bisects \angleC)

\therefore \triangle ABC \cong \triangleADC     (by ASA criterion)

AB = AD                                             (by CPCT)

BC = CD.                                            (by CPCT)

Hence proved.

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