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Assignment

Learn and apply the Triangle Proportionality Theorem to solve problems involving midsegments of triangles. Discover the relationship between midsegments, slopes, and lengths of sides. Includes a coordinate proof example.

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Assignment

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  1. Assignment • P. 298-301: 1-6, 8, 10, 12-19 some, 20, 21, 24, 29, 30, 36, 37, 47, 48 • Challenge Problems

  2. Triangle Proportionality Theorem

  3. Triangle Proportionality Theorem Set up a proportion and solve

  4. Warm-Up A midsegmentof a triangle is a segment that connects the midpoints of two sides of the triangle. Every triangle has 3 midsegments.

  5. 5.1 Midsegment Theorem and Coordinate Proof Objectives: • To discover and use the Midsegment Theorem • To write a coordinate proof

  6. Midsegment A midsegmentof a triangle is a segment that connects the midpoints of two sides of the triangle. Every triangle has 3 midsegments.

  7. Midsegment A midsegmentof a triangle is a segment that connects the midpoints of two sides of the triangle. Every triangle has 3 midsegments.

  8. Example 1 Graph ΔACE with coordinates A(-1, -1), C(3, 5), and E(7, -5). Graph the midsegment MS that connects the midpoints of AC and CE.

  9. Example 1 Now find the slope and length of MS and AE. What do you notice about the midsegment and the third side of the triangle?

  10. Midsegment Theorem The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side.

  11. Example 3 1. 2.

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