Core Connections Geometry Outline Chapter 5: Completing the Triangle Toolkit Core Lesson Homework Objectives Problems 5.1.1 2-5 7-12 5.1.2 13-14 Sine and Cosine Ratios 5.1.2 15 17-23 Selecting a Trig Tool 5.1.3 24-26 29-35 Inverse Trig 5.1.4 36-38 Trigonometric Applications 41-46 5.2.1 47-48 5.2.1 49 52-58 Special Right Triangles 5.2.2 59-61 64-70 Pythagorean Triples 5.3.1 72, 74, 75 77-82 5.3.2 84-85 Finding Missing Parts of Triangles 5.3.2 86 89-95 Law of Sines 5.3.3 96-97 100-105 Law of Cosines Choosing a Tool 5.3.5 118-125 126-138 Practice Test Practice Test Ch. 5 139-149 Closure Closure Activity Guiding Questions: How can I justify my conclusions? What is the relationship? Can I generalize the process? Is it always true? What information do I need? Is there another way? In this chapter, you will learn: How to recognize and use special right triangles. The trigonometric ratios of sine and cosine as well as the inverses of these functions. How to apply trigonometric ratios to find missing measurements in right triangles. New triangles tools called the Law of Sines and Law of Cosines. How to recognize when the information provided is not enough to determine a unique triangle. Geometry Chapter 5 Learning Targets Formative Learning Targets Self-Assessment 1. Inverse Trigonometry 1 2 3 4 5 6 7 8 9 10 I can use inverse trigonometry to find missing angle measure in right triangles. ____, ____, ____, ____ 2. Sine, Cosine, and Tangent 1 2 3 4 5 6 7 8 9 10 I can use sine, cosine, and tangent to find missing side lengths in right triangles. ____, ____, ____, ____ 3. Law of Sines and Law of Cosines 1 2 3 4 5 6 7 8 9 10 I can use Law of Sines and Law of Cosines to find missing side lengths in non-right triangles. ____, ____, ____, ____ 4. Solving Right Triangles (Special Right Triangles) 1 2 3 4 5 6 7 8 9 10 I can use 30o-60o-90o and 45o-45o-90o right triangle relationships to solve for missing side lengths and angle measures in a special right triangle. ____, ____, ____, ____ Summative Learning Targets 1. Arithmetic and Geometric Sequences 1 2 3 4 5 6 7 8 9 10 I can determine if a sequence is arithmetic or geometric. I can create a table for a sequence and use it to write an explicit rule for the sequence. ____, ____, ____, ____ 2. Solving Quadratic Equations 1 2 3 4 5 6 7 8 9 10 I can solve a quadratic equation by factoring or using the quadratic formula. ____, ____, ____, ____ 3. Similar Triangle Flowcharts 1 2 3 4 5 6 7 8 9 10 I can prove two triangles are similar using a flowchart. ____, ____, ____, ____ 4. Pythagorean Theorem 1 2 3 4 5 6 7 8 9 10 I can use the Pythagorean Theorem to solve for the missing side of a right triangle. ____, ____, ____, ____ 5. Probability 1 2 3 4 5 6 7 8 9 10 I can determine probabilities of unions, intersections, and complements. ____, ____, ____, ____ .