Question

ABC is an isosceles triangle with AB = AC and D is the mid-point of base BC (see figure).

1. State three pairs of equal parts in the triangles ABD and ACD.
2. Is ∆ABD ≅ ∆ACD. If so why?

Answer 1

a. In ∆ABD and ∆ACD,

AD = AD  ...(Common)

AB = AC  ...(Given)

BD = CD  ...(D is mid-point of BC)

b. Yes, by using (a) part, we get

∆ABD ≅ ∆ACD  ...(SSS criterion)