Given: EF¯¯¯¯¯¯¯¯≅GD¯¯¯¯¯¯¯¯

Question

, DE¯¯¯¯¯¯¯¯ ∥ FG¯¯¯¯¯¯¯¯¯

Prove: DEFG is a parallelogram.

Select the angle(s) that are consecutive with ∠G
.

(1 point)
Responses

∠E
∠E

∠D
∠D

∠F

Answer 1

To prove that DEFG is a parallelogram given that EF ≅ GD and DE ∥ FG, we will use the properties of parallel lines and congruent segments.

1. Given Information:

   • EF ≅ GD (segments are congruent)
   • DE ∥ FG (lines are parallel)

2. Proving that DEFG is a parallelogram:

   • Since DE is parallel to FG, and we have a transversal line (EF and GD) cut by these parallel lines, the alternate interior angles formed will be congruent.
   • The properties of a parallelogram state that if one pair of opposite sides is both parallel and congruent, then the quadrilateral is a parallelogram.
   • Here, since DE is parallel to FG and EF is congruent to GD, we have one pair of opposite sides (DE and FG) parallel and congruent, making DEFG a parallelogram.

Now, regarding the angles:

Given the angle ∠G, the consecutive angles are the angles that are adjacent to it. In a quadrilateral, consecutive angles are those located next to each other.

The angles adjacent to ∠G in quadrilateral DEFG are:

• ∠F (next to G)
• ∠D (other next to G)

Therefore, the responses to your question regarding which angles are consecutive with ∠G are:

• ∠F
• ∠D

Thus, the correct responses would be:

• ∠D
• ∠F