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Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a rectangle? a coordinate plane with quadrilateral ABCD at A negative 2 comma 0, B 0 comma negative 2, C negative 3 comma negative 5, D negative 5 comma negative 3 Prove that segments AD and AB are congruent and parallel. Prove that opposite sides are congruent and that the slopes of consecutive sides are equal. Prove that segments BC and CD are congruent and parallel. Prove that opposite sides are congruent and that the slopes of consecutive sides are opposite reciprocals

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ensiah193

Answer:

Prove that opposite sides are congruent and that the slopes of consecutive sides are opposite reciprocals

Step-by-step explanation:

In Quadrilateral ABCD with points A(-2,0), B(0,-2), C(-3,-5), D(-5,-3)

Using the distance formula

d =  sqrt(x2-x1)^2+(y2-y1)^2

|AB| = sqrt(0-(-2))^2+(-2-0)^2 = sqrt(8) = 2sqrt(2)

|CD| = sqrt(-5+3))^2+(-3+5)^2) = sqrt(8) = 2sqrt(2)

|BC| = sqrt(-3-0))^2+(-5+2)^2 = sqrt(18) = 3sqrt(2)

|AD| sqrt(-5+2)^2+(-3-0)^2 = sqrt(18) = 3sqrt(2)

Since |AB| is congruent to |CD| and |BC| is congruent to |AD|, we conclude that opposite sides are congruent.

Next, let us consider the slope.

Slope of |AB| = _-2-0_______ =__-2__  = -1

                          0-(-2)                     2

Slope of |BC| = __-5+2___ =    _-3___  =  1

                            -3-0                  -3

Since the slopes of consecutive sides are opposite reciprocals, therefore ABCD is a rectangle.

lhmarianateixeira

In this exercise we have to use the knowledge of triangles to calculate the opposite and congruent sides, in this way we find that:

Since |AB| is congruent to |CD| and |BC| is congruent to |AD|, we conclude that opposite sides are congruent.

So using the data informed in the exercise statement, we have that:

  • A(-2,0),
  • B(0,-2),
  • C(-3,-5),
  • D(-5,-3)

Using the distance formula:

[tex]d = \sqrt{(x_2-x_+1)^2+(y_2-y_1)^2} \\|AB| = \sqrt{(0-(-2))^2+(-2-0)^2} = 2\sqrt{2}\\|CD| = \sqrt{(-5+3))^2+(-3+5)^2)} = 2\sqrt{(2)}\\|BC| = \sqrt{(-3-0))^2+(-5+2)^2} = 3\sqrt{(2)}\\|AD|= \sqrt{(-5+2)^2+(-3-0)^2} = 3\sqrt{(2)}[/tex]

See more about triangles at brainly.com/question/25813512

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