Question

1. quadrilateral efgh is at e (-2, 3), f (1, 6), g (4, 3), and h (1, 0). given
2. ?
3. ef || gh
4. ?
5. ef and gh are perpendicular to fg
6. ?
7. quadrilateral efgh is a square

which of the following completes statement 4 of the proof?
ef, fg, gh, and eh are congruent
ef || gh
eh || fg
fg and eh are perpendicular to gh

Explanation:

Step1: Analyze the proof - context

We are proving a quadrilateral is a square. So far, we've shown side - lengths are equal and some parallel sides.

Step2: Recall properties of a square

A square has opposite sides parallel. We already have $\overline{EF}\parallel\overline{GH}$. We need to show the other pair of opposite sides are parallel.

Step3: Check the slopes

We calculate the slopes of $\overline{EH}$ and $\overline{FG}$. The slope of $\overline{EH}$ with $E(-2,3)$ and $H(1,0)$ is $m_{EH}=\frac{0 - 3}{1+2}=-1$. The slope of $\overline{FG}$ with $F(1,6)$ and $G(4,3)$ is $m_{FG}=\frac{3 - 6}{4 - 1}=-1$. Since $m_{EH}=m_{FG}=-1$, $\overline{EH}\parallel\overline{FG}$.

Answer:

C. $\overline{EH}\parallel\overline{FG}$