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ROCKY FORD CURRICULUM GUIDE SUBJECT: Geometry GRADE: High School Grade Level Expectation Evidence Outcome 1. Objects in the plane can be transformed, and those transformations can be described and analyzed mathematically a. Understand congruence in terms of rigid motions. i. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure. C ii. 1. Objects in the plane can be transformed, and those transformations can be described and analyzed mathematically Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. C Student-Friendly Learning Objective Level of Thinking Appl Appl iv. We will explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions Appl We will prove theorems about lines and angles. Appl Prove theorems about triangles. I We will prove theorems about triangles. Appl iii. Prove theorems about We will prove theorems Appl © Learning Keys, 800.927.0478, www.learningkeys.org KUTA Geometry Software We will use the definition of congruence in terms of rigid motions to decide if two figures are congruent. Appl ii. Academic Vocabulary Rigid motion We will use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. b. Prove geometric theorems. i. Prove theorems about lines and angles. I Resource Correlation Congruence We will use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure iii. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. C Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. C TIMELINE: 2nd Quarter KUTA Geometry Software Holt McDougal Geometry Teacher’s Edition pg 462470 Corresponding parts ASA SAS SSS Holt McDougal Geometry Teacher’s Edition pg 146220 Page 1 ROCKY FORD CURRICULUM GUIDE SUBJECT: Geometry Grade Level Expectation 2. Concepts of similarity are foundational to geometry and its applications GRADE: High School Evidence Outcome Student-Friendly Learning Objective parallelograms. I a. Define trigonometric ratios and solve problems involving right triangles. i. Explain that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. C about parallelograms. ii. Explain and use the relationship between the sine and cosine of complementary angles. C iii. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. C 1. Functions model situations where one quantity determines another and can be represented algebraically, graphically, and using tables f. Extend the domain of trigonometric functions using the unit circle. i. Use radian measure of an angle as the length of the arc on the unit circle subtended by the angle. C ii. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the © Learning Keys, 800.927.0478, www.learningkeys.org Level of Thinking TIMELINE: 2nd Quarter Resource Correlation Academic Vocabulary Trigonometric ratios We will explain that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. Appl Holt McDougal Geometry Teacher’s Edition pg 524583 Sine Cosine Tangent KUTA Geometric software Appl We will explain and use the relationship between the sine and cosine of complementary angles Appl Holt McDougal Geometry Teacher’s Edition pg 43, 348-358, 540-541 We will use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. We will extend the domain of trigonometric functions using the unit circle. We will explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Pythagorean theorem Holt McDougal Geometry Teacher’s Edition pg 570 Unit circle Radian Appl Comp KUTA Geometry Software Page 2 ROCKY FORD CURRICULUM GUIDE SUBJECT: Geometry Grade Level Expectation 2. Concepts of similarity are foundational to geometry and its applications GRADE: High School Evidence Outcome unit circle. C b. Prove and apply trigonometric identities. i. Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1. ? ii. Use the Pythagorean identity to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. C © Learning Keys, 800.927.0478, www.learningkeys.org Student-Friendly Learning Objective Level of Thinking We will prove the Pythagorean identity sin2(θ) + cos2(θ) = 1. Evaluate TIMELINE: 2nd Quarter Resource Correlation Academic Vocabulary Trigonometric identities Apply We will use the Pythagorean identity to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle Page 3