Question

in the given figure, AB=AD and angle BAC = angle DAC.Prove that triangle ABC and triangle ADC are congruent.Also state the criteria by which the two triangle will be congruent. ​

Answer 1

Answer:In Triangle ABC and Triangle ADC

AB= AD (Given)

∠BAC=∠DAC (Given)

AC=AC (Common)

Hence, Triangle ABC is congruent to Triangle ADC by SAS congruence rule.

Therefore ∠ACB=∠ACD by CPCT. So we know that AC bisects ∠C.

HOPE THIS HELPS YOU

Answer 2

Answer:

Given :- In figure, AD = AB and angle DAC = angle BAC .

To prove :- triangle ADC and triangle ABC

proof :- In triangle ADC and triangle ABC

AD = AB ( given)

AC = AC ( common )

angle DAC = angle BAC ( given )

By SAS congruence rule

triangle ADC is congruent to triangle ABC

Hence, proved

I hope it will help you