Question

In the diagram, DG I EF

What additional information would prove that DEFG is an
isosceles trapezoid?
y
5
D-22) G 1.2)
O DE GF
O DE DG
O EF DG
O EF = GF
E(-4,-3)
F(3-3)
5

Answer 1

The correct additional information is that EF = GF.

To prove that DEFG is an isosceles trapezoid, you need to show that either DE || FG or DE = FG.

Looking at the options:

- DE || DG: This is not sufficient information because it only tells us that DE and DG are parallel, but it doesn't provide any information about FG.

- DE = DG: This is not sufficient either because it only tells us that DE and DG have equal lengths, but it doesn't provide information about the parallelism with FG.

- EF = DG: This is not sufficient as it only states that EF and DG have equal lengths, but it doesn't give information about DE and FG.

- EF = GF: This is the option that would prove DEFG is an isosceles trapezoid. If EF is equal to GF, it means that the non-parallel sides DE and FG are equal in length, making DEFG an isosceles trapezoid.

Therefore, the correct additional information is that EF = GF.

Answer 2

a) DE ≅ GF

Explanation:

In the picture attached, the diagram is shown.

An isosceles trapezoid is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. In this case, the left and right side lengths are DE and GF, respectively; then they are congruent.