Question

9) In the equilateral triangle
ABC, AD and BE are the
medians on the sides BC
and CA respectively.
Show that AD = BE.
plz answer me quickly ​

Answer 1

Answer:

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 )

Answer 2

Step-by-step explanation:

area of triangle ABC is 1/2×AD×BC

also area of triangle ABC is 1/2×BE×CA

so 1/2×AD×BC=1/2×BE×CA

so. AD×BC=BE×CA

this triangle is equilateral so BC=CA

so. AD=BE