# Midsegment Theorem

__Developing Triangle Midsegment Theorem__

Notice the figure below:

How are D, E and F related to the sides of the triangle?

What do you conjecture?

Segment DE, DF and ER are all midsegments.

What do you notice about \(\overline{AC}\) and \(\overline{DE}\)? What angles are congruent?

- Draw a scalene triangle, \(Δ ABC\) as shown above,using a ruler, it may be helpful to do so on graph paper.
- Construct the midpoints of all three sides of your triangle, and connect them together to form a smaller triangle \(ΔDEF\).
- Measure the side lengths of \(Δ ABC\) and \(Δ BDE\). Compare them. What do you notice? Also compare the side lengths of \(ΔABC\) and \(ΔADF\).
- Summarize the midsegment theorem.