Verified Answer :

Answer: a) DE ≅ GF

Step-by-step explanation:

Since, in the isosceles trapezoid the non parallel sides are congruent.

Here, DEFG is a trapezoid in which,

DG║ EF,

⇒ DG and EF are the parallel sides,

⇒ DE and GF are non parallel sides,

Hence, by the above definition, the given trapezoid will be isosceles if DE and GF are congruent.

That is, DE ≅ GF

⇒ First option is correct.

In the diagram, DG ∥ EF , to prove that DEFG is an isosceles trapezoid Option (a) DE ≅ GF is CORRECT.

To prove  that DEFG is an isosceles trapezoid we need to check the each options accordingly.

Given: An isosceles trapezoid DEFG where, DG ∥ EF.

What is an isosceles trapezoid?

An isosceles trapezoid is a trapezoid where the base angles is equal  and therefore the left & right side lengths are also equal. Here in the isosceles trapezoid the non parallel sides are congruent.

According to the figure DEFG is an isosceles trapezoid where,

DG║ EF,

  • DG and EF sides are parallel.
  • DE and GF sides are non parallel sides.

Hence according to the above definition the trapezoid will be isosceles only if DE & GF are congruent.

= DE ≅ GF

Therefore,Option (a) DE ≅ GF is CORRECT.

Learn more about Congruency here :https://brainly.com/question/2949762

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