Question

In triangle ABC it is given that AB=AC,and BM and CN are medians and meet at point O ,angle COM=BON,angle COM=angle 2OBC.prove that triangle BMA= CNA

Answer 1

In Δ ABC, 
AB = AC (given)                                             ∴Δ ABC is an isosceles triangle 
so ∠ABC = ∠ACB
∴ ∠BMA = ∠CNA
as in isosceles and equilateral triangles, a median bisects any angle at a vertex whose two adjacent sides are equal in length.
∠BAM =∠CNA (cpct)
∴ ΔBMA = ΔCNA 

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