Question

ad is the median of an isoscelos triangle abc in which AB=AC prove that ∆abd~ to ∆acd

Answer 1

In ∆abd &∆adc
•Ab=AC(given)
•Angle b=angle c(angles opp. To equal sides are always equal)
•Bd=cd(ad is median)
By SSA congruence rule
∆abd~∆adc

Answer 2

In triangle abd and triangle acd,

1. AB=AC(sides of an isosceles triangle)

2. BD=DC(since AD bisects BC)

3. AD is common to both triangles.

Thus, triangle ABD~triangle ACD(by, S. S. S)