Question

part b. show that the quadrilateral is a parallelogram.
because ( ef = gh = \boxed{1} ), ( overline{ef} cong \boxed{2} ). because these are ( \boxed{3} ) line segments, their slopes are ( \boxed{4} ) and they are parallel. ( overline{ef} ) and ( \boxed{5} ) are ( \boxed{6} ) that are both congruent and parallel. so, ( efgh ) is a parallelogram by the ( \boxed{7} ).

options: 0, 1, 3, 4, 6, 8, ( overline{fg} ), ( overline{he} ), ( overline{gh} ), horizontal, vertical

Explanation:

Step1: Fill length of EF, GH

$EF = GH = 8$

Step2: Fill congruent segment

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

Step3: Identify segment orientation

These are horizontal line segments

Step4: Fill slope value

Horizontal slopes are $0$

Step5: Pair second congruent sides

$\overline{EF}$ and $\overline{FG}$

Step6: Identify second pair orientation

They are vertical that are both congruent and parallel

Step7: State parallelogram theorem

By the Both Pairs of Opposite Sides Congruent and Parallel Theorem

Answer:

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