SOLUTION: Hello. My question: prove that thesegment connecting the midpoints of legs of an isosceles trapezoid is parallel to the bases of the trapezoid. I know the slope formula but I do no

Algebra ->  Length-and-distance -> SOLUTION: Hello. My question: prove that thesegment connecting the midpoints of legs of an isosceles trapezoid is parallel to the bases of the trapezoid. I know the slope formula but I do no      Log On


   

Question 728807: Hello. My question: prove that thesegment connecting the midpoints of legs of an isosceles trapezoid is parallel to the bases of the trapezoid. I know the slope formula but I do not know what to put in the equation. I think we are supposed to use variable coordinates. Thanks!
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Let me describe an approach for this.

Draw your isosceles trapezoid with longer base at the bottom, shorter base at the top. Make the left endpoint of the longer, lower-positioned base at the origin, (0, 0). Let coordinate of other endpoint of the longer base be at (0,a).

Now for the top, shorter base, let's say left endpoint x is at d, and y is at h. This left endpoint has coordinates (d,h). The RIGHT-HAND coordinate of this base would be at x=a-d, y=h, or (a-d, h). Be sure you draw this on paper, and label all four points and the x and y axes.

Hopefully you are satisfied that you drew an isosceles trapezoid.

Now, use the midpoint formula to get the coordinates of the midpoint of the lefthand leg and the midpoint of the righthand leg. You should be able to find that the y value of each midpoint is the same for each leg. This means the slope of the line connecting these midpoints is zero, as is the slope of the top and bottom bases, therefore all three segments are parallel.