Question

in the diagram, (overline{dg} parallel overline{ef})
what additional information would prove that defg is an isosceles trapezoid?
(\bigcirc) (overline{de} cong overline{gf})
(\bigcirc) (overline{de} cong overline{dg})
(\bigcirc) (overline{ef} cong overline{dg})
(\bigcirc) (overline{ef} cong overline{gf})

Explanation:

Step1: Recall isosceles trapezoid rule

A trapezoid with one pair of parallel sides is isosceles if its non-parallel sides are congruent. Here, $\overline{DG} \parallel \overline{EF}$, so non-parallel sides are $\overline{DE}$ and $\overline{GF}$.

Step2: Match to option

We need $\overline{DE} \cong \overline{GF}$ to confirm it is isosceles.

Answer:

$\overline{DE} \cong \overline{GF}$