# How do you prove this theorem on trapezoids and its median? The median (or mid-segment) of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.

The proof of this theorem about mid-segment of a trapezoid is below.

End of proof.

The lecture dedicated to this and other properties of quadrilaterals as well as many other topics are addressed by a course of advanced math for high school students at Unizor.

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To prove the theorem on trapezoids and their medians:

- Draw a trapezoid ABCD where AB is parallel to DC.
- Draw the median EF, where E is the midpoint of AD and F is the midpoint of BC.
- Use the properties of triangles and parallel lines to show that EF is parallel to AB and DC.
- Show that EF is one half the sum of the lengths of the bases AB and DC.
- Prove that AE is congruent to ED and BF is congruent to FC.
- Use the segment addition postulate to show that EF = AE + BF = ED + FC = 1/2(AD + BC).

- Conclude that the median EF of the trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.

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