Question

in the diagram, \\( \overline { d g } \parallel \overline { e f } \\).
what additional information would prove that defg is an
isosceles trapezoid?
\\( \bigcirc \overline { d e } \cong \overline { g f } \\)
\\( \bigcirc \overline { d e } \cong \overline { d g } \\)
\\( \bigcirc \overline { e f } \cong \overline { d g } \\)
\\( \bigcirc \overline { e f } \cong \overline { g f } \\)

Explanation:

Step1: Recall the definition of an isosceles trapezoid

An isosceles trapezoid is a trapezoid (a quadrilateral with one pair of parallel sides) where the non - parallel sides (the legs) are congruent. In trapezoid \(DEFG\) with \(DG\parallel EF\), the non - parallel sides are \(DE\) and \(GF\).

Step2: Check the congruence of non - parallel sides

We need to show that the non - parallel sides \(DE\) and \(GF\) are congruent. The condition \(\overline{DE}\cong\overline{GF}\) would make \(DEFG\) an isosceles trapezoid.

Answer:

\(\overline{DE}\cong\overline{GF}\) (the first option)