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Home > CCG > Chapter 12 > Lesson 12.1.2 > Problem 12-23

12-23.

In Chapter 7, you discovered that the midsegment of a triangle is not only parallel to the third side, but also half its length. But what about the midsegment of a trapezoid?

The diagram at right shows a midsegment of a trapezoid. That is, is a midsegment because points and are both midpoints of the non-base sides of trapezoid .

  1. If , and , find the coordinates of points and . Then compare the lengths of the bases ( and ) with the length of the midsegment . What seems to be the relationship?

    How do you find the lengths from coordinates?
    Think of how the answers could be related.

    It seems to be the average of and .

  2. See if the relationship you observed in part (a) holds if , and .

    Use the same method you used to solve part (a).

  3. Write a conjecture about the midsegment of a trapezoid.

    The midsegment of a trapezoid is parallel to the bases and has a length that is the average of the lengths of the bases.

A trapezoid, A, B, C, D where side D, C, is parallel to side A, B. Midpoint between A, D is point E.  Midpoint between C, B is point F. Line E, F is drawn.

Use the eTool below to help solve the problem.
Click the link at right for the full version of the eTool: CCG 12-23 HW eTool