Hauptinhalt
Nebraska Math
High School Advanced Topics: GEOMETRY
Students will solve problems and reason with geometry using multiple representations, make connections within math and across disciplines, and communicate their ideas.
Apply the Law of Sines and the Law of Cosines to find unknown measures in triangles.
- General triangle word problems
- Laws of sines and cosines review
- Solve triangles using the law of cosines
- Solve triangles using the law of sines
- Solving for a side with the law of cosines
- Solving for a side with the law of sines
- Solving for an angle with the law of cosines
- Solving for an angle with the law of sines
- Trig word problem: stars
Determine the three-dimensional object created by rotating or revolving a two-dimensional object about an axis.
Determine the shape of a two-dimensional cross-section of a three-dimensional object.
Use Cavalieri’s Principle to determine volume of three-dimensional figures.
Identify symmetry properties of a function (e.g., axis of symmetry of a parabola) and know the connection between its symmetry properties and specific transformations.
- Function symmetry introduction
- Intro to function symmetry
- Intro to parabola transformations
- Parabolas intro
- Scale & reflect parabolas
- Scaling & reflecting parabolas
- Sine & cosine identities: symmetry
- Symmetry of algebraic models
- Symmetry of algebraic models
- Symmetry of polynomials
- Tangent identities: symmetry
Recognize that translations can be described in terms of vectors.
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Find the images and preimages of transformations of a point, shape, or relation on the coordinate plane, where transformations include the following compositions: reflections about lines of any rational slope passing through the origins, delations about the origin by any positive scale factor, and translations.
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Explain the focus-directrix construction of a parabola and derive the equation of a parabola from focus and directrix for a parabola whose axis of symmetry is a coordinate axis.
Use known definitions and results in informal argumentation to construct logical arguments.
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Distinguish between empirical reasoning, examples, and deductive reasoning, as well as informal and formal reasoning.
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Evaluate the deductive consequences of alternative definitions of known objects (e.g., whether a trapezoid is defined as a quadrilateral with exactly one pair of parallel sides or defined as at least one pair of parallel sides).
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