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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. |
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