GEOM 3 | Lesson 3 | Explore (Midsegment Theorem)

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.

Try This!

Go to Try This! (Midsegment Theorem)