Which would show that \( F G H J \) is a parallelogram? Select all that apply. A. Show that slope of \( \overline{F G}= \) slope of \( \overline{H J} \) and \( F G=H J \). B. Show that slope of \( \overline{F G}= \) slope of \( \overline{H J} \) and \( F J=G H \). \( \square \) C. Show that slope of \( \overline{F G}= \) slope of \( \overline{H J} \) and slope of \( \overline{F J}= \) slope of \( \overline{G H} \) D. Show that \( F G=H J \) and \( F J=G H \).

To determine which options would show that \( F G H J \) is a parallelogram, we need to recall the properties of parallelograms. A quadrilateral is a parallelogram if: 1. Both pairs of opposite sides are equal in length. 2. Both pairs of opposite sides are parallel (which can be shown by having equal slopes). 3. One pair of opposite sides is both equal in length and parallel. Now, let's analyze each option: **A.** Show that slope of \( \overline{F G}= \) slope of \( \overline{H J} \) and \( F G=H J \). - This option shows that one pair of opposite sides (\( F G \) and \( H J \)) are both equal in length and parallel. This is sufficient to prove that \( F G H J \) is a parallelogram. **B.** Show that slope of \( \overline{F G}= \) slope of \( \overline{H J} \) and \( F J=G H \). - This option shows that one pair of opposite sides (\( F G \) and \( H J \)) are parallel, and the other pair (\( F J \) and \( G H \)) are equal in length. This is also sufficient to prove that \( F G H J \) is a parallelogram. **C.** Show that slope of \( \overline{F G}= \) slope of \( \overline{H J} \) and slope of \( \overline{F J}= \) slope of \( \overline{G H} \). - This option shows that both pairs of opposite sides are parallel. This is sufficient to prove that \( F G H J \) is a parallelogram. **D.** Show that \( F G=H J \) and \( F J=G H \). - This option shows that both pairs of opposite sides are equal in length. This is also sufficient to prove that \( F G H J \) is a parallelogram. Based on this analysis, the options that would show that \( F G H J \) is a parallelogram are: - **A** - **B** - **C** - **D** Thus, all options (A, B, C, and D) apply.