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Exploring Proportions and Similar Triangles in Real-World Applications

Discover the practical use of similar triangles in professions like architecture and engineering. Learn the Triangle Proportionality Theorem and Side-Splitting Theorem, followed by practice problems and examples. Explore other proportions in triangles using properties and exchange methods.

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Exploring Proportions and Similar Triangles in Real-World Applications

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  1. Warm-up • What do you think the use of similar triangles is in the “real-world”? • What professions could use it? Today Warm-up Objective Guided notes Hwk: 7.5 Practice Problems

  2. 7.5: Proportions and Similar Triangles Obj: ____________________ ________________________

  3. Theorems, Postulates, & Definitions 8.4 The Side-Splitting Theorem Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other 2 sides, then it divides the other two sides proportionally. Ex: In QRS, if TU // QS then R T U Q S

  4. In this triangle, AB CD Find x. TOC 8.4 The Side-Splitting Theorem Example Use the Side-Splitting Theorem to solve problems involving triangles.

  5. Other Proportions in ABC • We can use the properties of proportions (exchange) to create “new” true proportions. AE = DE AB BC AE= AB DE BC A E B D C AE = AB AE = AD AD AC AB AC

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