Question

In the figure, AABC is an isoceles trangle in which AB=A6, Also D is a point such that BP = CD prove that AD-bisects angle A and Angle D ​

Answer 1

Answer:

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.

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