Question

question 2 of 25
in the diagram below, fg = 10 and hj = 10. which additional facts would guarantee that fghj is a parallelogram? check all that apply.
a. fj = 15, gh = 15
b. fg is parallel to hj
c. gh = 10
d. fj = 10, gh = 15

Explanation:

Step1: Recall parallelogram properties

A quadrilateral is a parallelogram if both pairs of opposite - sides are equal or if one pair of opposite sides is both parallel and equal.

Step2: Analyze option A

If $FJ = 15$ and $GH=15$, then both pairs of opposite sides are equal ($FG = HJ = 10$ and $FJ=GH = 15$), so it is a parallelogram.

Step3: Analyze option B

If $\overline{FG}$ is parallel to $\overline{HJ}$ and $FG = HJ=10$, then one pair of opposite sides is both parallel and equal, so it is a parallelogram.

Step4: Analyze option C

If $GH = 10$, we only know that $FG=HJ = 10$ and $GH = 10$. We don't have enough information about the fourth - side $FJ$ to guarantee it's a parallelogram.

Step5: Analyze option D

If $FJ = 10$ and $GH = 15$, the opposite sides are not equal in pairs, so it is not a parallelogram.

Answer:

A. $FJ = 15, GH = 15$
B. $\overline{FG}$ is parallel to $\overline{HJ}$