Question

HELP PLEASE 100 POINTS AND BRAINLIEST!

Answer 1

Answer:

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

Step-by-step explanation:

Let us verify the choosen option

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

Using the distance formula

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$|AB|=\sqrt{(0-(-2))^2+(-2-0)^2}=\sqrt{8}=2\sqrt{2}\\|CD|=\sqrt{(-5+3))^2+(-3+5)^2}=\sqrt{8}=2\sqrt{2}\\|BC|=\sqrt{(-3-0))^2+(-5+2)^2}=\sqrt{18}=3\sqrt{2}\\|AD|=\sqrt{(-5+2)^2+(-3-0)^2}=\sqrt{18}=3\sqrt{2}$

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|= $\frac{-2-0}{0-(-2)} =\frac{-2}{2}=-1$

Slope of |BC|$=\frac{-5+2}{-3-0} =\frac{-3}{-3}=1$

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

Option D is the correct option.

Answer 2

Answer:

the answers will be D

Step-by-step explanation:

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