Question

show that quadrilateral is a parallelogram. because ef = gh = 1 8, \overline{ef} \cong \overline{gh}. because these are 3 horizontal line segments, their slopes are 4 0 and they are parallel. \overline{ef} and 5 \overline{fg} are 6 vertical that are both congruent and parallel. so, efgh is a parallelogram by the 7 opposite sides parallel and congruent theorem. (options at the bottom: \overline{gh}, horizontal, vertical, undefined, definition of a parallelogram, parallelogram opposite sides converse, opposite sides parallel and congruent theorem, parallelogram diagonals converse, opposite sides, bisected diagonals)

Explanation:

Step1: Correct length value

$EF = GH = 8$

Step2: Confirm congruent segments

$\overline{EF} \cong \overline{GH}$

Step3: Identify segment orientation

These are horizontal line segments

Step4: Slope of horizontal segments

Their slopes are $0$

Step5: Identify second pair of sides

$\overline{EF}$ and $\overline{GH}$ are opposite sides

Step6: Confirm side orientation match

They are horizontal (not vertical)

Step7: Apply parallelogram theorem

By the Opposite Sides Parallel and Congruent Theorem, $EFGH$ is a parallelogram.

Answer:

1. $8$
2. $\overline{GH}$
3. horizontal
4. $0$
5. $\overline{GH}$
6. horizontal
7. Opposite Sides Parallel and Congruent Theorem