G.3.5 Lesson Summary
Let's examine a segment whose endpoints are the midpoints of 2 sides of the triangle. If D is the midpoint of segment BC and E is the midpoint of segment BA, then what can we say about ED and triangle ABC?
Segment ED is parallel to the third side of the triangle and half the length of the third side of the triangle. For example, if AC = 10, then ED = 5. This happens because the entire triangle EBD is a dilation of triangle ABC with a scale factor of 1/2.
In triangle ABC, segment FG divides segments AB and CB proportionally. In other words, BG/GA = BF/FC. Again, there is a dilation that takes triangle ABC to triangle GBF, so FG is parallel to AC and we can calculate
its length using the same scale factor.
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)