Question

Ivan used coordinate geometry to prove that quadrilateral EFGH is a square. Figure EFGH is shown. E is at negative 2, 3. F is at 1, 6. G is at 4, 3. H is at 1, 0. Statement Reason 1. Quadrilateral EFGH is at E (−2, 3), F (1, 6), G (4, 3), and H (1, 0) 1. Given 2.___?___ 2.segment EF E (−2, 3) F (1, 6) d equals the square root of the quantity 1 plus 2 all squared plus 6 minus 3 all squared d equals the square root of the quantity 3 squared plus 3 squared equals the square root of 18 equals 3 times the square root of 2 segment FG F (1, 6) G (4, 3) d equals the square root of the quantity 4 minus 1 all squared plus 3 minus 6 all squared d equals the square root of the quantity 3 squared plus negative 3 squared equals the square root of 18 equals 3 times the square root of 2 segment GH G (4, 3) H (1, 0) d equals the square root of the quantity 1 minus 4 all squared plus 0 minus 3 all squared d equals the square root of the quantity negative 3 squared plus negative 3 squared equals the square root of 18 equals 3 times the square root of 2 segment EH E (−2, 3) H (1, 0) d equals the square root of the quantity 1 plus 2 all squared plus 0 minus 3 all squared d equals the square root of the quantity 3 squared plus negative 3 squared equals the square root of 18 equals 3 times the square root of 2 3. segment EF is parallel to segment GH 3. segment EF E (−2, 3) F (1, 6) m equals 6 minus 3 over 1 plus 2 equals 3 over 3 equals 1 segment GH G (4, 3) H (1, 0) m equals 0 minus 3 over 1 minus 4 equals negative 3 over negative 3 equals 1 4. ___?___ 4. segment EH E(−2, 3) H (1, 0) m equals 0 minus 3 over 1 plus 2 equals negative 3 over 3 equals negative 1 segment FG F (1, 6) G (4, 3) m equals 3 minus 6 over 4 minus 1 equals negative 3 over 3 equals negative 1 5. segment EF and segment GH are perpendicular to segment FG 5. The slope of segment EF and segment GHis 1. The slope of segment FG is −1. 6. ___?___ 6. The slope of segment FG and segment EH is −1. The slope of segment GH is 1. 7. Quadrilateral EFGH is a square 7. All si

Answer 1

An answer option that correctly completes statement 4 of the proof include the following: C. EH || FG.

What are parallel lines?

In Mathematics and Euclidean Geometry, parallel lines refers to two lines that are always the same distance apart and never meet.

This ultimately implies that, two (2) lines are parallel under the following conditions:

Slope of line 1, = Slope of line 2,

Based on the information provided about quadrilateral EFGH, we can logically deduce that it represents a square and as such, all of its sides have a slope of -1. Therefore, any parallel segment within it must have a slope of -1;

EF || GH (step 3)

EH || FG (step 4)