Dates Standards/Essential Questions Essential Knowledge/Skills/Understanding Resources Block Standard: G.8 Essential Understanding Key Vocabulary The Pythagorean Theorem is essential for solving angle of depression The student will solve real-world problems involving right triangles. angle of elevation 7.5days 15 days problems involving right triangles by area of a triangle The relationships between the sides and angles of right using the Pythagorean Theorem and cosine triangles are useful in many applied fields. its converse, properties of special right hypotenuse Some practical problems can be solved by choosing an triangles, and right triangle Pythagorean Theorem trigonometry. efficient representation of the problem. right triangle The ratios of side lengths in similar right triangles sine (adjacent/hypotenuse or opposite/hypotenuse) are tangent Prerequisite/Extension SOL independent of the scale factor and depend only on the trigonometry 8.10 a) verify the Pythagorean angle the hypotenuse makes with the adjacent side, thus 45°-45°-90° triangle Theorem; b) apply the Pythagorean justifying the definition and calculation of trigonometric 30°-60°-90° triangle Theorem functions using the ratios of side lengths for similar A.3 express sq roots/cube roots of right triangles. whole numbers/the square root of DOE Lesson Essential Knowledge/Skills monomial alg exp (simplest radical form) Determine whether a triangle formed with three given A.4 solve multistep linear/ quad lengths is a right triangle. equation (2 vars) a) solve literal ‐ Solve for missing lengths in geometric figures, using Textbook Resources equation; b) justify steps used in properties of 45-45-90 triangles. simplifying expresessions and solving Chapter 8: 8.1 8.5 – equations; c) solve quad equations Solve for missing lengths in geometric figures, using (alg/graph); d) solve multistep linear properties of 30-60-90 triangles. Resources/Lessons equations (alg/graph) Solve problems involving right triangles, using sine, cosine, and tangent ratios. Solve real-world problems, using right triangle trigonometry and properties of right triangles. Explain and use the relationship between the sine and cosine of complementary angles
Dates Standards/Essential Questions Essential Knowledge/Skills/Understanding Resources Block 7.5days 15 days Standard: G.8 The student will solve real-world problems involving right triangles by using the Pythagorean Theorem and its converse, properties of special right triangles, and right triangle trigonometry. Prerequisite/Extension SOL 8.10 a) verify the Pythagorean Theorem; b) apply the Pythagorean Theorem A.3 express sq roots/cube roots of whole numbers/the square root of monomial alg exp (simplest radical form) A.4 solve multistep linear/ quad equation (2 vars) ‐ a) solve literal equation; b) justify steps used in simplifying expresessions and solving equations; c) solve quad equations (alg/graph); d) solve multistep linear equations (alg/graph) Essential Understanding The Pythagorean Theorem is essential for solving problems involving right triangles. The relationships between the sides and angles of right triangles are useful in many applied fields. Some practical problems can be solved by choosing an efficient representation of the problem. The ratios of side lengths in similar right triangles (adjacent/hypotenuse or opposite/hypotenuse) are independent of the scale factor and depend only on the angle the hypotenuse makes with the adjacent side, thus justifying the definition and calculation of trigonometric functions using the ratios of side lengths for similar right triangles. Essential Knowledge/Skills Determine whether a triangle formed with three given lengths is a right triangle. Solve for missing lengths in geometric figures, using properties of 45-45-90 triangles. Solve for missing lengths in geometric figures, using properties of 30-60-90 triangles. Solve problems involving right triangles, using sine, cosine, and tangent ratios. Solve real-world problems, using right triangle trigonometry and properties of right triangles. Explain and use the relationship between the sine and cosine of complementary angles Key Vocabulary angle of depression angle of elevation area of a triangle cosine hypotenuse Pythagorean Theorem right triangle sine tangent trigonometry 45°-45°-90° triangle 30°-60°-90° triangle DOE Lesson Textbook Resources Chapter 8: 8.1 – 8.5 Resources/Lessons
2014-2015_geometry_completed_pacing_guide.docx