Question

The table contains the proof of the theorem of the relationship between slopes of parallel lines. What is the missing statement in step 2?











BC = EF, AB = DE







BC × AB = -(EF × DE)

Answer 1

Slope is the gradient of line. The missing statement in step 2 is to substitute the value of both the slopes to each other.

What is Slope?

A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

Given to us

BC = EF, AB = DE

If we draw a vertical and a horizontal line, with respect to line AC and DF which are the parallel lines, we will get two triangles along the lines as shown in the image below.

In ΔABC and ΔDEF,

The slope of line AC and EF can be written as,

$AC = \dfrac{AB}{BC}$                  $DF = \dfrac{DE}{EF}$

We know that the slope of both the line is the same, therefore,

$AC =DF$

Substitute the value of slopes,

$\dfrac{AB}{BC} =\dfrac{DE}{EF}\\\\{AB \times EF}= {BC \times DE}$

Substitute the values of BC = EF, AB = DE,

${AB \times BC}= {EF\times DE}$

Hence, the missing statement in step 2 is to substitute the value of both the slopes to each other.

Learn more about Slopes:

https://brainly.com/question/3605446