Question

In the given figure, ABC is an isosceles triangle in which AB = AC. Also, D is a point
such that BD = CD. Prove that AD bisects ∠A and ∠D.

Answer 1

Answer:

Step-by-step explanation:

Given :

△ABC is an isosceles triangle.

AB=AC

BD=CB

To prove :

AD bisects ∠A and ∠D

Proof :

Consider △ABD and △ACD

⇒  AB=AC                    [ Given ]

⇒  BD=CD                   [ Given ]

⇒  AD=AD                   [ Common side ]

∴   △ABD≅△ACD                      [ By SSS congruence property ]

⇒  ∠BAD=∠CAD                    [ C.P.C.T ]

⇒  ∠BDA=∠CDA                    [ C.P.CT. ]

Hence, we have proved that AD bisects ∠A and ∠D.