Respuesta :
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:
[tex]\dfrac{4-2}{-3-2} =-\dfrac{2}{5}[/tex]
The slope of the line segment AD is:
[tex]\dfrac{-4-(-2)}{3-(-2)} =\dfrac{-4+2}{3+2}=-\dfrac{2}{5}[/tex]
The slope of the line segment CD is:
[tex]\dfrac{2-(-4)}{2-3} =\dfrac{2+4}{2-3}=\dfrac{6}{-1}=-6[/tex]
The slope of the line segment BA is:
[tex]\dfrac{4-(-2)}{-3-(-2)} =\dfrac{4+2}{-3+2}=\dfrac{6}{-1}=-6[/tex]
Because the slopes of parallel lines are equal. Therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.
