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Lesson 7.4, Right Triangle Similarity

Lesson 7.4, Right Triangle Similarity. Altitude. Altitude : Ex: Construct an altitude from each vertex:. Similar Right Triangles. Similar Right Triangles : Ex: ∆ ~ ∆ ~ ∆. A B B D. A B D. C C. Practice.

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Lesson 7.4, Right Triangle Similarity

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  1. Lesson 7.4, Right Triangle Similarity

  2. Altitude • Altitude: • Ex: Construct an altitude from each vertex:

  3. Similar Right Triangles • Similar Right Triangles:Ex: ∆ ~ ∆ ~ ∆ A B B D A B D C C

  4. Practice • ∆ABC is split by altitude AD into two smaller right triangles. • Draw ∆ABD and ∆DBC • Write a similarity statement for the three right triangles A 12 5 B 13 C

  5. Side Proportions • Side Proportions: Short = ShortMid = MidLong LongLongLong, etc.

  6. Practice • What is the length of each unknown side? A B 6 C C x 8 y 8 B D 17

  7. Practice • Complete each proportion: AC = BCAB = yAC = yBC x BC x x BD A B C C B D

  8. Practice • What is the value of each variable? A B D C y z 5 12 x

  9. Practice

  10. Lesson 7.5 – Proportions in Triangles

  11. Side-Splitter and Angle-Bisector Theorems Q R S T U • Side-Splitter Theorem: • Angle Bisector Theorem: A B C D

  12. Practice • What is the value of each variable? A B C D A B C D E 3 4 8 x 5 9 8 y

  13. Practice • What is the value of each variable? A B C D Q R S T U 6 12 y 8 x 7 5 4

  14. SOL Question #25

  15. SOL Question

  16. Chapter 8 Preparations Geometric Mean and Reducing Radicals

  17. Geometric Mean • Mean: • Arithmetic Mean: • Geometric Mean:

  18. Practice • What are the Arithmetic and Geometric means of each pair of numbers?4 and 85 and 15

  19. Practice • What are the Arithmetic and Geometric means of each pair of numbers?4 and 85 and 15

  20. Homework • Lesson 7.4, #5 – 19 oddLesson 7.5, #9 – 29 odd • Lesson 8.1 #17 – 35 oddLesson 8.2, #7 – 11 odd

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