Lesson 7 4 Right Triangle Similarity Altitude Altitude

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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:

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

Similar Right Triangles • Similar Right Triangles: Ex: ∆ ~∆ ~∆ A A B

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

Practice • ∆ABC is split by altitude AD into two smaller right triangles. –

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 B 5 13 C

Side Proportions • Side Proportions: Short = Short Long Mid = Mid Long, etc.

Side Proportions • Side Proportions: Short = Short Long Mid = Mid Long, etc.

Practice • What is the length of each unknown side? A 6 x C

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

Practice • Complete each proportion: AC = BC AB = y BC x A

Practice • Complete each proportion: AC = BC AB = y BC x A B C B AC = y x BD C D

Practice • What is the value of each variable? A y B 5 12

Practice • What is the value of each variable? A y B 5 12 z Dx C

Practice

Practice

Lesson 7. 5 – Proportions in Triangles

Lesson 7. 5 – Proportions in Triangles

Side-Splitter and Angle-Bisector Theorems Q • Side-Splitter Theorem: R S T • Angle Bisector

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

Practice • What is the value of each variable? A 3 A B 5

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

Practice • What is the value of each variable? A Q 5 T x

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

SOL Question #25

SOL Question #25

SOL Question

SOL Question

Chapter 8 Preparations Geometric Mean and Reducing Radicals

Chapter 8 Preparations Geometric Mean and Reducing Radicals

Geometric Mean • Mean: • Arithmetic Mean: • Geometric Mean:

Geometric Mean • Mean: • Arithmetic Mean: • Geometric Mean:

Practice • What are the Arithmetic and Geometric means of each pair of numbers?

Practice • What are the Arithmetic and Geometric means of each pair of numbers? 4 and 8 5 and 15

Practice • What are the Arithmetic and Geometric means of each pair of numbers?

Practice • What are the Arithmetic and Geometric means of each pair of numbers? 4 and 8 5 and 15

Homework • Lesson 7. 4, #5 – 19 odd Lesson 7. 5, #9 –

Homework • Lesson 7. 4, #5 – 19 odd Lesson 7. 5, #9 – 29 odd • Lesson 8. 1 #17 – 35 odd Lesson 8. 2, #7 – 11 odd

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