Question

In the figure, AB and CD are perpendiculars on BD. Also AB=CD and AF=CE. Prove that BE=FD.

Answer 1

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Answer 2

BE=FD.

GIVEN: AB and CD are perpendiculars on BD. Also AB=CD and AF=CE.
TO PROVE BE=FD.
SOLUTION:
As we are given in the question,

AB and CD are perpendicular to BD.

It is also given that,

AB=CD.

AF=CE.

As we know,

In triangle ABF and CDE,

∠B = ∠D = 90°.                     [ 90 EACH]

AB = CD.

AF = CE.

Therefore,

Triangle ABF ≅ CDE.

Using the Side Angle Side congruence(SAS),

From this we get,

BF = DE { Corresponding parts of congruent triangles)

From this, it can be implied,

BF = EF = DE = EF.

Hence,

BE = FD.

Hence Proved.

#SPJ2.