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Geometry

Today: Class Attendance / Announcements Warm Up Homework Questions / Check 8.5 Notes / Practice Memory Review. Geometry. I've got a theory that if you give 100 percent all of the time, somehow things will work out in the end. Larry Bird. Warm Up.

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Geometry

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  1. Today: Class Attendance / Announcements Warm Up Homework Questions / Check 8.5 Notes / Practice Memory Review Geometry I've got a theory that if you give 100 percent all of the time, somehow things will work out in the end. Larry Bird

  2. Warm Up To be done individually! Raise your hand if you have a question!

  3. 8.5 – Proving Triangles are Similar • Objectives: • Prove triangles similar by SSS Similarity Theorem • Prove triangles similar by SAS Similarity Theorem • Use similar triangles in real life • Vocabulary: • SSS~, SAS~

  4. Side-Side-Side (SSS) Similarity Theorem A P Q R B C If the corresponding sides of two triangles are proportional, then the triangles are similar. , then ABC ~ PQR. If

  5. Which triangles are similar? M A P 15 25 20 6 8 10 R Q 18 O 24 N C B 30 What is the similarity statement? ABC ~ MNO ~ PQR 5:4 (ABC:MNO), 5:3 (ABC:PQR), and 4:3 (MNO:PQR) What is the scale factor?

  6. If an angle of one triangle is congruent to an angle of a second triangle, and the lengths of the sides including these angles are proportional, then the triangles are similar. X M N P Y Z Side-Angle-Side (SAS) Similarity Theorem If and , then XYZ ~ MNP.

  7. If AC = 6, AD = 10, BC = 9, CE = 6, is ∆ACB ~ ∆DCE? A Yes; by the SAS Similarity Theorem E C D B What is the scale factor? 3:2

  8. Given: ∆XYZ: XY = 5, YZ = 4, m<Z = 50° ∆UVW: UV = 10, VW = 8, m<W = 50° Are these triangles similar? If yes, what is the scale factor? If yes, what is the similarity statement? No, because the given angle is not the included angle.

  9. If EC = 9, AC = 18, KI = 18, DI = 36, m<C = m<I = 98°, are the triangles similar? K I A C E D 1:2 What is the scale factor? What is the similarity statement? AEC ~ DKI

  10. You are mounting a projector to the ceiling. If a projected image is 1.5’ tall from 5’ away, how far should you mount it if you want a 10’ tall projection? 33.3 feet

  11. To find the distance across a lake you form two similar isosceles triangles. What is the length of the lake? 180’ 120’ 90’ 240 feet

  12. Assignment: 8.5 pgs. 492-495 #1-5, 10-18, 32-37 Chapter 8 Test on Monday or Tuesday! Vote tomorrow! Geometry I've got a theory that if you give 100 percent all of the time, somehow things will work out in the end. Larry Bird

  13. Additional Examples: 11 feet A museum worker is attempting to check the dinosaur’s eyes. Unfortunately, the snout is too wide and he can not get a clear view. To get a better look, he places a mirror on the ground and uses the reflections. If the worker’s eyes are 5.5’ high and the mirror is 12’’ from the man and 2’ from the dinosaur, what is the height of the dinosaur?

  14. Additional Examples: Given: ∆PQR: PQ = 22.5, QR = 12, PR = 13.5 ∆STU: ST = 30, TU = 16, SU = 18 Yes, by SSS Similarity Theorem Are these triangles similar? If yes, what is the scale factor? If yes, what is the similarity statement? 4:3 AEC ~ DKI

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