Altitude • Altitude: • Ex: Construct an altitude from each vertex:
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. – 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.
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 B C B AC = y x BD C D
Practice • What is the value of each variable? A y B 5 12 z Dx C
Practice
Lesson 7. 5 – Proportions in Triangles
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 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 7 R S 6 B 4 U 12 y C 8 D
SOL Question #25
SOL Question
Chapter 8 Preparations Geometric Mean and Reducing Radicals
Geometric Mean • Mean: • Arithmetic Mean: • Geometric Mean:
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? 4 and 8 5 and 15