Question

if two medians of a triangle then prove that triangle is equilateral​

Answer 1

To prove that : AC = BC
O is the centroid ( point at which medians meet) of the triangle ABC . & centroid O divides each median in the ratio 2:1
median AD = median BE ( given)
=> 2/3 AD = 2/3 BE
=> AO = BO . . . . . . . (1)
& 1/3 AD = 1/3 BE
=> OD = OE . . . . . . .(2)
< AOE = < BOD ( vertically opposite angle) . . (3)
By (1),(2),(3)
Tri OAE congruent to tri OBD (by SAS congruence theorem)
=> AE = BD ( cpct ) . . . . .(4)
=> but AE = EC & BD = DC ( as median bisects opposite sides)
=> EC = DC . . . . . . .(5)
=> AE + EC = BD + DC
=> AC = BC
=> tri CAB is an isosceles triangle
[ proved]