Triangles and Trigonometry Unit Overview/Essential Understanding: Students will: Use and extend similarity properties to explore and justify conjectures about geometric figures Derive, extend, and use the Pythagorean Theorem Identify and apply patterns from right triangles to solve meaningful problems, including, special right triangles (45-45-90 and and triangles with sides that are Pythagorean triples Develop, apply, and justify triangle similarity relationships, such as trigonometric ratios using a variety of methods Unit Objectives: At the end of this module, students will be able to independently use their learning to: Use the Pythagorean Theorem Use the Converse of the Pythagorean Theorem Use the properties of 45-45-90 triangles Use the properties of 30-60-90 triangles Find trigonometric ratios using right triangles Use trigonometric ratios to find measures in triangle Focus Standards Addressed in this Unit: CC.2.2.HS.C.9 Prove the Pythagorean Identity and use it to calculate trigonometric ratios – CC.2.3.HS.A.7 Apply trigonometric ratios to solve problems involving right triangles – Important Standards Addressed in this Unit: CC.2.3.HS.A.14 Apply geometric concepts to model and solve real-world problems – Misconceptions: Trig ratios only apply to right triangles Concepts/Content: Competencies/Skills: Description of Activities: The Pythagorean Theorem and Use the Pythagorean Theorem Direct teacher-led instruction Its Converse Use properties of special right Large group Q & A discussion Special Right Triangles triangles Independent student work Trigonometry Use trigonometry to find missing group collaboration measures of triangles Online remedial/enrichment videos Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test Interdisciplinary Connections: Additional Resources: N/A Glencoe Geometry Textbook
Triangles and Trigonometry Unit Overview/Essential Understanding: Students will: Use and extend similarity properties to explore and justify conjectures about geometric figures Derive, extend, and use the Pythagorean Theorem Identify and apply patterns from right triangles to solve meaningful problems, including, special right triangles (45-45-90 and and triangles with sides that are Pythagorean triples Develop, apply, and justify triangle similarity relationships, such as trigonometric ratios using a variety of methods Unit Objectives: At the end of this module, students will be able to independently use their learning to: Use the Pythagorean Theorem Use the Converse of the Pythagorean Theorem Use the properties of 45-45-90 triangles Use the properties of 30-60-90 triangles Find trigonometric ratios using right triangles Use trigonometric ratios to find measures in triangle Focus Standards Addressed in this Unit: CC.2.2.HS.C.9 – Prove the Pythagorean Identity and use it to calculate trigonometric ratios CC.2.3.HS.A.7 – Apply trigonometric ratios to solve problems involving right triangles Important Standards Addressed in this Unit: CC.2.3.HS.A.14 – Apply geometric concepts to model and solve real-world problems Misconceptions: Trig ratios only apply to right triangles Concepts/Content: The Pythagorean Theorem and Its Converse Special Right Triangles Trigonometry Competencies/Skills: Use the Pythagorean Theorem Use properties of special right triangles Use trigonometry to find missing measures of triangles Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work group collaboration Online remedial/enrichment videos Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test Interdisciplinary Connections: N/A Additional Resources: Glencoe Geometry Textbook
2017-Geometry-BHASD-Math-Curriculum.docx