Question

in a quadrilateral ABCD. AB = AD and AC bisects angle A show that ∆ABC is congruent to ∆ ABD..

Answer 1

Given : quadrilateral ABCD. AB = AD and AC bisects angle A

To Find : Show that ∆ABC ≅ ∆ ADC..

Solution:

AC bisects angle A

=> ∠BAC = ∠DAC = ∠A/2

compare ∆ABC and ∆ ADC..

AC =  AC  common

∠BAC = ∠DAC

AB = AD  given

hence

∆ABC ≅ ∆ ADC..  ( SAS)

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