Question

in the diagram, dg || ef. what additional information would prove that defg is an isosceles trapezoid?
ef || gf
ef || dg
de || dg
de || gf

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 of the trapezoid are congruent. Since \(DG\parallel EF\) (given), if we can show that \(DE\cong GF\), then by the definition of an isosceles trapezoid (\(DEFG\) is a trapezoid with \(DG\parallel EF\) and the non - parallel sides \(DE\) and \(GF\) congruent), \(DEFG\) is an isosceles trapezoid.

Answer:

\(DE\cong GF\)