 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Session 5, Part C:
The Midline Theorem (55 minutes)

In This Part: The Midline Cut | Some Geometry Facts | Proving the Midline Theorem

In this part, we will begin to use segment notation. Optional: About Segment Notation.

Let's look again at how we solved Problem B3, in which we dissected a triangle to form a parallelogram. Note 4

Find the midpoints of two sides of a triangle. Cut along the segment connecting those two midpoints. Rotate the top triangle 180° about one of the midpoints. The two segments match because the cut was at the midpoint. The following are the conjectures that we will prove in the midline theorem:

 • Quadrilateral ABCD is a parallelogram because the opposite sides are the same length. AD and BC are the same length because they were made by cutting at a midpoint. • AB and CD are the same length because a midline cut makes a segment half as long as the base.

Here are examples of midline cuts for four triangles (regular, right, isosceles, obtuse):   Triangle Midline Cut Rotate Top Triangle                      Session 5: Index | Notes | Solutions | Video