This sample material consists of Investigations 2 and 3 from Lesson 2, "Triangles and Trigonometric Ratios." In Investigation 2, students explore conditions that guarantee two triangles are similar and special cases of similar right triangles. The trigonometric ratios sine, cosine, and tangent are introduced. In the third investigation, students use trigonometric ratios for indirect measurement in several different contexts.
Throughout the curriculum, interesting problem contexts serve as the foundation for instruction. As lessons unfold around these problem situations, classroom instruction tends to follow a common pattern as elaborated under Instructional Design.
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In Course 3, students develop the ability to reason formally in geometric settings. Deductive reasoning is used to prove theorems concerning parallel lines and transversals, angle sums of polygons, similar and congruent triangles and their application to special quadrilaterals, and necessary and sufficient conditions for parallelograms.
In Course 4, geometry and algebra become increasingly intertwined. Students develop understanding of two-dimensional vectors and their applications and the use of parametric equations in modeling linear, circular, and other nonlinear motion. In addition, students intending to pursue programs in the mathematical, physical, and biological sciences, or engineering extend their ability to visualize and represent three-dimensional surfaces using contours, cross sections, and reliefs to visualize and sketch surfaces and conic sections defined by algebraic equations.
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