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

`(q - r)/(m- n) = (p - s)/(m - n)`

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 = (y_2 - y_1)/(x_2 - x_1)`

So, we have:

`m = (q - r)/(m- n)`

Next, the slope of AD using:

`m = (y_2 - y_1)/(x_2 - x_1)`

So, we have:

`m = (p - s)/(m - n)`

For ABCD to be a parallelogram; then:

`(q - r)/(m- n) = (p - s)/(m - n)`