Question

Stan knows that segment AB∥segment CD. He wants to use the definition of a parallelogram to prove that quadrilateral ABCD is a parallelogram. Which equation can he use?

Answer 1

Answer:

$\frac{q - r}{m- n} = \frac{p - s}{m - n}$

Step-by-step explanation:

Given

See attachment for parallelogram

Required

Proof that ABCD is a parallelogram

We know that opposite sides are equal and parallel.

First, we calculate the slope of BC

$m = \frac{y_2 - y_1}{x_2 - x_1}$

So, we have:

$m = \frac{q - r}{m- n}$

Next, the slope of AD using:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

So, we have:

$m = \frac{p - s}{m - n}$

For ABCD to be a parallelogram; then:

$\frac{q - r}{m- n} = \frac{p - s}{m - n}$