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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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