Answer:
(A)Segment EF, segment FG, segment GH, and segment EH are congruent
Step-by-step explanation:
<u>Step 1</u>
Quadrilateral EFGH with points E(-2,3), F(1,6), G(4,3), H(1,0)
<u>Step 2</u>
Using the distance formula
Given E(-2,3), F(1,6)
Given F(1,6), G(4,3)
Given G(4,3), H(1,0)
Given E (−2, 3), H (1, 0)
<u>Step 3</u>
Segment EF ,E (−2, 3), F (1, 6)
Slope of |EF|=
Segment GH, G (4, 3), H (1, 0)
Slope of |GH|
<u>Step 4</u>
Segment EH, E(−2, 3), H (1, 0)
Slope of |EH|
Segment FG, F (1, 6,) G (4, 3)
Slope of |EH|
<u>Step 5</u>
Segment EF and segment GH are perpendicular to segment FG.
The slope of segment EF and segment GH is 1. The slope of segment FG is −1.
<u>Step 6</u>
<u>Segment EF, segment FG, segment GH, and segment EH are congruent. </u>
The slope of segment FG and segment EH is −1. The slope of segment GH is 1.
<u>Step 7</u>
All sides are congruent, opposite sides are parallel, and adjacent sides are perpendicular. Quadrilateral EFGH is a square