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Chapter 8 mini unit

Learn how to use proportions to find missing values in similar triangles and explore the concept of similarity in polygons. Discover the Triangle Similarity Theorems (AA, SAS, SSS) and the Side Splitter Theorem.

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Chapter 8 mini unit

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  1. Chapter 8 mini unit

  2. Learning Target • I can use proportions to find missing values of similar triangles.

  3. 8-1 Solving Proportions

  4. Similarity • Two figures that have the same shape but not necessarily the same size are similar () • Two polygons are similar if all of their angles are congruent and their corresponding sides have the same scale factor

  5. 8-2 Similar Polygons

  6. Are the polygons similar? If so, write a similarity statement and state the similarity ratio

  7. On 8-2, work on #1-12

  8. The polygons are similar, find the missing value

  9. Do 8-2 #13-23

  10. 8.3 Triangle Similarity Theorems • AA • SAS • SSS

  11. In the following problems, if the triangles are similar, state why and write a similarity statement.

  12. On 8-3, do #1-6

  13. Explain why the triangles are similar and find the value of x

  14. On 8-3, do #7-12 skip 11(unless you want a challenge)

  15. Warmup

  16. 8.4 SIMILARITY IN RIGHT TRIANGLES

  17. Finding the geometric mean of two numbers • Geometric mean of two numbers a and b is

  18. Find the geometric mean of 4 and 18 • Find the geometric mean of 15 and 20

  19. Do 8-4 #1-6

  20. Notes • The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. • Which triangles Are similar?

  21. Notes • The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse. EX:

  22. Geometric Mean Example

  23. Find the value of x

  24. Find the value of x

  25. Find the missing variables

  26. 8.5 Proportions in Triangles

  27. Side Splitter Theorem • If a line is parallel to one side of a triangle and intersects the other two sides then it divides those sides proportionally (Examples on next slide)

  28. Side Splitter Theorem

  29. TRIANGLE ANGLE BISECTOR THEOREM If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle

  30. REVIEW FOR QUIZ (Paper Review) or? • P.419 12-21,66 • P.426 9-16, 21-28 • P.436 4-19 • P.442 1-8, 15-20 • P.448 1-3, 11-16

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