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GSE Analytic Geometry-A Week 12: 10/24/2016 – 10/28/2016 Georgia Standards of Excellence: MCC9-12.G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. MCC9-12.G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor: (a) A dilation takes a line not passing through the center of dilation to a parallel line, and leaves a line passing through the center unchanged. (b) The dilation of a line segment is longer or shorter in the ratio given by the scale factor. MCC9-12.G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. MCC9-12.G.SRT.3 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. MCC9‐12.G.SRT.6 Understand that by similarity, side ratios in triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. MCC9-12.G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles MCC9‐12.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Standards for Mathematical Practice: MP 1 Make sense of problems and persevere in solving them. MP 5 Use appropriate tools strategically. MP 2 Reason abstractly and quantitatively. MP 6 Attend to precision. MP 3 Construct viable arguments and critique the reasoning of others. MP 7 Look for and make use of structure. MP 4 Model with mathematics. MP 8 Look for and express regularity in repeated reasoning. Differentiation Strategies: Lesson notes, guided instruction, list of Common Pythagorean Triples and their multiples, mnemonic device to help memorize the trig functions, graphic organizer Vocabulary: Pythagorean theorem, simplest radical form, acute angle, complementary angles, trigonometric functions, sine, cosine, tangent Monday Essential Question: What do you know about similarity? Activity: Quiz #5 Assignment #54: Complete Similarity Review Part B #1-11 Tuesday Essential Question: How do you simplify radicals? How can you find the third side of a right triangle? Opening: Turn in Assignment #54, Homework Check 11, review simplifying radicals Activity: Students will recall the Pythagorean Theorem and use it so solve problems. Introduce Pythagorean triples. Review converse, discuss and use the Converse of the Pythagorean Theorem. Closing: Lesson Quiz Assignment #55: p.300-303 #1-3,5-8,15-16,19-21,38-40,48,49 Wednesday Essential Question: How do you simplify radicals? How can you find the third side of a right triangle? Activity: Practice simplifying radicals and using the Pythagorean Theorem Assignment #56: Simplifying Radicals and The Pythagorean Theorem Practice Thursday Essential Question: How do side ratios in right triangles define trigonometric ratios? Opening: Review Assignment #55 and #56 Activity: Review AA~ Postulate. Review right triangles. Discuss the acute angles of a right triangle. Introduce the trigonometric ratios. Practice finding trig ratios, calculating trig ratios and using trig ratios to find lengths. Closing: Application Problem Assignment #57: p.321 #21-27,31-43,53,68-70; for questions #22-36, round all answers to the nearest ten-thousandth. Friday Essential Question(s): How is the sine ratio of one acute angle in a right triangle related to the cosine ratio of the other acute angle? Opening: Review Assignment #57 Activity: Discover the relationship of the sine and cosine ratios of the acute angles of a right triangle. Use trig functions to solve real-world problems. Closing: Lesson Quiz Assignment #58: p.322 #49-50,62-65; p.326 #3-15odd