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.
