SOLUTION: Prove that if a triangle has two congruent medians, then it is isosceles.

Question 23437: Prove that if a triangle has two congruent medians, then it is isosceles.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
LET ABC be THE TRIANGLE WITH BE AND CF AS THE MEDIANS ,WE ARE GIVEN THAT BE=CF.
LET BE AND CF MEET AT G THE CENTROID.
CONSIDER TRIANGLES ECG AND FBG ......WE HAVE
GE=BE/3=CF/3=GF.....(SINCE MEDIANS ARE TRISECTED AT CENTROID AND BE=CF IS GIVEN)
GC=2CF/3=2BE/3=GB...(SINCE MEDIANS ARE TRISECTED AT CENTROID AND BE=CF IS GIVEN)
ANGLE EGC=ANGLE FGB.....(VERTICALLY OPPOSITE ANGLES)
HENCE THE 2 TRIANGLES ARE CONGRUENT OR IDENTICAL.....
HENCE BF=CE
BUT BF=BA/2 AND CE=CA/2...SINCE BE AND CF BEING MEDIANS E AND F ARE MIDPOINTS OF AC AND AB.
HENCE BA=2BF=2CE=CA
HENCE THE TRIANGLE IS ISOCELLES
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