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igor_vitrenko [27]
2 years ago
13

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

SAT
1 answer:
Darina [25.2K]2 years ago
8 0

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:

brainly.com/question/25926201

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