Question

Ivan used coordinate geometry to prove that quadrilateral efgh is a square.

Answer 1

A square has parallel opposite sides, and congruent four sides.

The coordinates of the square are given as:

$E = (-2,3)$

$F=(1,6)$

$G =(4,3)$

$H = (1,0)$

Calculate the distance between the vertices of the square using the following distance formula

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_1)^2}$

So, we have:

$E F= \sqrt{(-2- 1)^2 + (3- 6)^2}$

$EF = \sqrt{18}$

$FG= \sqrt{(4- 1)^2 + (3- 6)^2}$

$FG= \sqrt{18}$

$GH = \sqrt{(4 -1)^2 + (3 - 0)^2}$

$GH = \sqrt{18}$

$HE = \sqrt{(1--2)^2 + (0 -3)^2}$

$HE = \sqrt{18}$

Notice that all the side lengths of the square are the same.

Hence, the quadrilateral EFGH is square

Read more about squares at:

https://brainly.com/question/25926201

Answer 2

Answer:

What is the Slope of Parallel Lines?

The slope of parallel lines are always equal. Therefore, this means that if two segments have the same slope value, then both segments must be parallel to each other.

In the proof shown, EH and FG have the same slope values which is -1. This implies they are parallel to each other.

Hope its helpful!