Question

Given: AC bisects angle BCD , Angle ABC is congruent to angle ADC prove AB is congruent to AD. Help immediately

Answer 1

AC bisects ∠BAD, => ∠BAC=∠CAD ..... (1)

thus in ΔABC and ΔADC,    ∠ABC=∠ADC (given),

                                      ∠BAC=∠CAD      [from (1)],

AC (opposite side side of ∠ABC) = AC (opposite side side of ∠ADC), the common side between ΔABC and ΔADC

Hence,      by AAS axiom, ΔABC ≅ ΔADC,

Therefore,  BC (opposite side side of ∠BAC) = DC (opposite side side of ∠CAD),  since (1)

Hence, BC=DC proved.

Answer 2

Answer:

Solution given;

<BCA=<ACD

<ABC=<ADC

now

In traingle ABC & ∆ ACD

AC=AC[common base]

<BCA=<ACD[bisector bisect it]

<ABC=<ADC[Given]

∆ABC is congruent to ∆ ACD by S.A.A. axiom

AB is congruent to AD.

[ corresponding sides of a congruent triangle are equal]

Hence proved.