Question

ABC is an isosceles triangle in which AB = AC. BE and CF are its two medians. Show that BE = CF.

Answer 1

ABC is an isosceles triangle (given) 

AB = AC (given) 

BE and CF are two medians (given) 

To prove: BE = CF 

In △CFB and △BEC 

CE = BF (Since, AC = AB = AC/2 = AB/2 = CE = BF) 

BC = BC (Common)

∠ECB = ∠FBC (Angle opposite to equal sides are equal)

By SAS theorem: △CFB ≅ △BEC 

So, BE = CF (By c.p.c.t)