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Warm-up

Warm-up. What triangle structures do Similarity and Congruence have in common? Which structures are used only for Congruence? Which structures are used only for Similarity? Why are the ones for congruence not used for Similarity. Can I haz similarity?. A tale of many kittens….

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Warm-up

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  1. Warm-up • What triangle structures do Similarity and Congruence have in common? • Which structures are used only for Congruence? • Which structures are used only for Similarity? • Why are the ones for congruence not used for Similarity

  2. Can I haz similarity? A tale of many kittens…

  3. Two ways to think about similarity • Things you can say once you alreadyknow two shapes are similar • How to determinewhether or not two figures are similar

  4. If you know two shapes are similar: • You can use the similarity statement to: • Identify Corresponding Parts • Create proportions • Determine congruent Correct! Incorrect!

  5. If you know two shapes are similar: • You can use the similarity statement to: • Identify Corresponding Parts • Create proportions • Determine congruent angles Correct! Incorrect!

  6. If you know two shapes are similar: • You can use the similarity statement to: • Identify Corresponding Parts • Create proportions • Determine congruent angles Correct! Incorrect!

  7. If you know two shapes are similar: • You can use the similarity statement to: • Identify Corresponding Parts • Create proportions • Determine congruent angles Next

  8. If you know two shapes are similar: • You can use the similarity statement to: • Identify Corresponding Parts • Create proportions • Determine congruent angles 1 2 3

  9. In order to show two figures are similar • You need to: • Identify Corresponding parts • Create Proportions • Identify Congruent Angles • Using one of the following “structures” • AA • SAS • SSS

  10. Corresponding… kittens?

  11. Which pair of cats are corresponding? Why?

  12. Quality/Quantity VS. Structure • “Biggest side” (Quantity or quality of the side) vs. • “The included side of the smallest and medium angles” (Location of the side in the structure of the triangle) • Note: Structure makes use of quantity and quality, but just goes a step further.

  13. Ratios: One item over another We usually try to compare two things that correspond

  14. Ratios, Proportion, Similarity, and Congruence • If two ratios are equal, we say they are proportional • If all of the corresponding sides of a figure are proportional, the figuresare similar. • If two figuresare similar, their corresponding angles are congruent.

  15. Any questions?

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