ABCD is an equilateral triangle. AD and BE are the medians on the side BC and CA respectively. Show that AD=BE.
Answers:
AC = BC {Sides of an Equilateral Triangle}
E and D is the mid point of AC and BC
{ BE and AD are median }
So, CE = EA = CD = BD
Now, In Triangle ABE and Triangle ABD
AC = BD (Mention Above)
/_A= /_B (60°)
AB = AB (Common)
So, Triangle ABE congurent to Triangle ABD.
( by S.A.S criteria)
Therefore,BE = AD ( by CPCT )