Question

in fig 7.16,AX is the bisector of triangle BAD and triangle BCD.prove that AB=AD​

Answer 1

Given: ∆ ABC, ∆ ADC, AX is the angle bisector of angles BAD and BCD.

To prove: AB = AD.

Proof:

In ∆ ABC and ∆ ADC,

angle BAC = angle DAC .... (given)

angle BCA = angle DCA .... (given)

AC = AC .... (common side)

Thus, ∆ ABC is congruent to ∆ ADC.

Therefore, by cpct,

AB = AD

Hence, proved.

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