Question

In the adjoining figure AB is parallel to CD and AB = CD. If E is the midpoint of BC, prove that triangle ABE is congruent to triangle DCE

#PleaseSolve
#QualityAnswersNeeded
#HelpWillBeAppreciated​

Answer 1

Given:

AB is parallel to CD.

AB = CD.

E is the mid-point of BC.

To Prove:

∆ ABE = ∆ DCE

Proof:

In ∆ ABE and ∆ DCE,

AB = CD ( Given )

angle AEB = angle CED = 90° ( Vertically Opposite Angles )

BE = CE ( E is the mid-point of BC )

Answer:

∆ ABE = ∆ DCE ( By SAS congruency rule )

SAS Congruency Rule:

If two triangles have equal measures of two sides and one angle then the two traingles are equal.

Answer 2

Answer:

May be the answer of this question is.

In a triangle ABE and DCE.

AB=CD(given)

BE=CE(because E is the perpendicular bisector of BC)

Angle ABE = Angle DCE (V. O. A)

So triangle ABE is congruent to triangle DCE ( by S. A. S criterion).

Hope it's helpful to you.

According to my point of view this is the correct answer.