Question

Complete the proof to show that ABCD is a parallelogram.

Answer 1

The slope of BC is
(4-2)/(-3-2) = -2/5

The slope of AD is 
(-2- -4)/(-2-3) = -2/5

The slope of CD is
(2- -4)/(2-3) = -6

The slope of BA is
(4- -2)/(-3- -2) = -6
 
BC ∥ AD and CD ∥ BA because their slopes are equal. Therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.

Answer 2

Answer: From the given figure

A=(-2,-2) , B=(-3,4),C=(2,2)and D=(3,-4)

We know that

Slope of a line =$\frac{y_2-y_1}{x_2-x_1}$

∴Slope of AB=$\frac{4-(-2)}{-3-(-2)} =\frac{6}{-1}=-6$

Slope of BC=$\frac{2-4}{2-(-3)} =\frac{-2}{5}$

Slope of CD=$\frac{-4-2}{3-2} =\frac{-6}{1} =-6$

Slope of AD=$\frac{-4-(-2)}{3-(-2)} =\frac{-2}{5}$

⇒AB is parallel to CD and BC is parallel to AD because slope of AB=slope of CD=-6 and slope of BC=slope of AD=[tex]\frac{-2}{5}[/tex]

Therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.