In triangle ABC shown below, point A is at (0,0) point B is at (x subscript2, 0)
point C is ([x sub1]/ 2, [y sub1]/2
point D is [x sub1 + xsub2]/2, ysub1/2)

Prove that segment DE is parallel to segment AB.

Proof below

Step-by-step explanation:

To prove DE and AB are parallel, we compare the slopes of both segments

Suppose we know a line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

Segment AB goes through the points (0,0) and (x2,0), thus:

The slope is 0 because the line is horizontal.

Now for the segment DE, the endpoints are

The slope is:

Segment DE is also horizontal, thus is parallel to segment AB.

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.