Question

Complete the proof to show that ABCD is a parallelogram. On a coordinate plane, quadrilateral A B C D is shown. Point A is at (negative 2, negative 2), point B is at (negative 3, 4), point C is at (2, 2), and point D is at (3, negative 4). The slope of Line segment B C is StartFraction 4 minus 2 Over negative 3 minus 2 EndFraction = negative two-fifths The slope of Line segment A D is StartFraction negative 4 minus (negative 2) Over 3 minus (negative 2) EndFraction = StartFraction negative 4 + 2 Over 3 + 2 EndFraction = negative two-fifths The slope of Line segment C D is StartFraction 2 minus (negative 4) Over 2 minus 3 EndFraction = StartFraction 2 + 4 Over 2 minus 3 EndFraction = StartFraction 6 Over negative 1 EndFraction = negative 6 The slope of Line segment B A is StartFraction 4 minus (negative 2) Over negative 3 minus (negative 2) EndFraction = StartFraction 4 + 2 Over negative 3 + 2 EndFraction = StartFraction 6 Over negative 1 EndFraction = negative 6 and because the ________________________________. Therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.

Answer 1

Answer:

Slopes of parallel lines are equal

Step-by-step explanation:

On a coordinate plane, quadrilateral ABCD is shown. Point A is at (-2, -2), point B is at (-3, 4), point C is at (2, 2), and point D is at (3, -4).

The slope of the line segment BC is:  

$\dfrac{4-2}{-3-2} =-\dfrac{2}{5}$

The slope of the line segment AD is:

$\dfrac{-4-(-2)}{3-(-2)} =\dfrac{-4+2}{3+2}=-\dfrac{2}{5}$

The slope of the line segment CD is:

$\dfrac{2-(-4)}{2-3} =\dfrac{2+4}{2-3}=\dfrac{6}{-1}=-6$

The slope of the line segment BA is:

$\dfrac{4-(-2)}{-3-(-2)} =\dfrac{4+2}{-3+2}=\dfrac{6}{-1}=-6$

Because the slopes of parallel lines are equal. Therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.