Abcd Is Equilateral Triangle Ad And Be Are Medians On Side And Respectively Show That Ad Be

ABCD is an equilateral triangle. AD and BE are the medians on the side BC and CA respectively. Show that AD=BE.


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 )