Question

in the given figure angle abc is an equilateral triangle here BD and CE are marion's show that BD is equal to CE

fast please ​

Answer 1

Given: ABC is an equilateral triangle.

           BD and CE are two medians of the equilateral triangle ABC.

To Find: BD = CD

Solution: ABC is an equilateral triangle.

So AB = BC = AC

Let us consider that, AB = BC = AC = x

As BD and CE are medians to the triangle, then

⇒AD = CD, AE = BE

Now, In triangles BDC and BCE we have,

BC ( Common Side )

CD = BE ( As AC = AB )

And 1/2AB = 1/2 AC ( As ABC is an equilateral triangle )

So by the SAS congruence criterion, we get that

Triangle BDC ≅ Triangle BCE

⇒ BD = CE ( Proved )