Question

In ∆ABC, is an isosceles triangle such that AB = AC and AD is median to BC. Which criteria we use to prove ∆ ∆ BAD CAD ≅ ?​

Answer 1

Answer:

By using angle bisector theorem,if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides : AD is median so BD = CD and in isosceles triangle AB = AC.

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Answer 2

Given :  ∆ABC   is an isosceles triangle such that AB = AC and

AD is median to BC.

To Find : Which criteria we use to prove ∆ BAD  ≅ ∆  CAD  

Solution:

∆ BAD  and ∆  CAD  

AB = AC    Given

AD = AD    Common

BD = CD  = BC/2  as AD is the median

Using side - side - side congruence property

∆ BAD  ≅ ∆  CAD  

Hence SSS  congruence is the correct answer

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