# 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?

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