Question

in the given figure AE=DE,CE=BE,then prove that AB =CD

Answer 1

In triangle AEB and triangle CDE
AE=DE
BE=CE
Angle AEB=Angle CED
Therefore triangle AEB is congruent to triangle CDE
Then AB=CD(CPCT)

Answer 2

AB = CD Proved

Step-by-step explanation:

Given : AE=DE    and    CE=BE

To Prove  :  AB =CD

Proof:

Since BC and AD are two straight lines.

∠AEB + ∠AEC = 180°(straight angle)   ⇒equation 1

Again, ∠CED + ∠AEC = 180°(straight angle)   ⇒equation 2

So, equation 1 = equation 2

∴ ∠AEB + ∠AEC = ∠CED + ∠AEC

Since ∠AEC is common on both side, then we can say that;

∠AEB  = ∠CED   ⇒equation 3

Now In ΔAEB and ΔDEC,

AE=DE  (given)

∠AEB  = ∠CED   (from equation 3)

CE=BE   (given)

So, By S.A.S. congruence property,

ΔAEB ≅ ΔDEC

Therefore AB = CD (By corresponding part of congruence triangle)

AB = CD  Hence Proved.