Question

Given a quadrilateral DEFG. If angle ED is supplementary to ____________then DEFG is a parallelogram .

A. angle EFG and angle DEF B. angle DGF and angle EFC C. angle DEF and angle DGF

Answer 1

The correct option is A.

Explanation:

It is given that DEFG is a parallelogram.

Draw the diagonals DF and EG. Place point H where DF and EG intersect.

In triangle HGD and HEF

,

∠HGD ≅ ∠HEF (Alternate Interior angle)

∠HDG ≅ ∠HFE (Alternate Interior angle)

By the definition of a parallelogram, the opposite sides of a parallelogram are congruent.

DG ≅ EF (Opposite sides of parallelogram)

According to ASA postulate :

two triangles are congruent if any two angles and their included side are equal in both triangles.

So, by using ASA criterion for congruence we get,

ΔDGH ≅ ΔFEH

Since corresponding sides of congruent triangles are congruent, therefore

GH ≅ EH (CPCTC)

DH ≅ FH (CPCTC)