Question

in the above image , AB=AC, triangle BAD= triangle CAD. Is triangle ABD =triangle ACD​

Answer 1

Answer:

△ABD and △ACD

AB=AC  (given )

Then ∠ABD=∠ACD ( because AB=AC )

and  ∠ADB=∠ADC=90( because AD⊥BC )

∴△ABD=△ACD

∠BAD=∠CAD

It is defective to use ∠ABD=∠ACD for proving this result

Answer 2

Answer:

In △ABC, we have

AB=AC⇒∠ABC=∠ACB

(angles opposite to equal sides.)

Again in △DBC, we have

DB=DC (given)

⇒∠DBC=∠DCB (angles opposite to equal sides).

Hence we obtain

∠ABC−∠DBC=∠ACB−∠DCB.

This gives

∠ABD=∠ACD. [henceproved]