Question

In the given figure,AB=BC and AD=EC.Prove that BD=BE.

Answer 1

Answer: Triangle ADB is congruent to CEB by S.A.S congruence criterion so BD = BE

Step-by-step explanation:

In triangles ADB and CEB,

AD=EC

AB=BC

Angle BAC = Angle BCA [AB=BC,so ABC is an isosceles triangle. In an isosceles triangle, angles opposite to equal sides are equal.]

So, triangle ADB is congruent to CEB.

Then, by c.p.c.t, BD=BE

-Proved

Answer 2

Step-by-step explanation:

AD=EC

addDEbothsides

AD+DE=EC+DE

AE=CD

In triangleABE and triangles DBC

BA=BC

angleA=angleC angles opp to equal sides are equal

AE=CD

triangleABEis concerrent totriangleDBC bySAS