Question

Prove segment DE is parallel to segment AB

Answer 1

We can compare the slopes of the two segments. Two segments (and two lines in general) are parallel if they have the same slope. The slope is computed as

`m_(AB) = \cfrac{\Delta y}{\Delta x} = \cfrac{B_y-A_y}{B_x-A_x}`

In this case, we have

`m_(AB) = \cfrac{0-0}{x_2-0} = 0`

and

`m_(DE) = \cfrac{(y_1)/(2)-(y_1)/(2)}{(x_1+x_2)/(2) - (x_1)/(2)} = 0`

Since both segments have the same slope, namely 0, they are parallel.