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Sagot :

The ABEF is a parallelogram because DC is extended to point F; AB ≅ FE and FA ≅ BE.

What is parallelogram?

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

We have ABCD is a parallelogram.

BE is perpendicular to FC

FA is perpendicular to FC

As we know in the parallelogram ABCD:

AB ≅ DC

AD ≅ CB

As the DC is extended to F

So, AB ≅ FE

And BE is perpendicular to FC

       FA  is perpendicular to FC  (given)

∴ FA ≅ BE

∴ ABEF is a parallelogram.

Thus, the ABEF is a parallelogram because DC is extended to point F; AB ≅ FE and FA ≅ BE.

Learn more about the parallelogram here:

brainly.com/question/1563728

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