Search the California Content Standards

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Understand similarity in terms of similarity transformations.

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Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar.

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Prove theorems involving similarity. [Focus on validity of underlying reasoning while using variety of formats.]

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Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally and conversely; the Pythagorean Theorem proved using triangle similarity.

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Prove theorems involving similarity. [Focus on validity of underlying reasoning while using variety of formats.]

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Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

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Define trigonometric ratios and solve problems involving right triangles.

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Understand 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.

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Define trigonometric ratios and solve problems involving right triangles.

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Explain and use the relationship between the sine and cosine of complementary angles.

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Define trigonometric ratios and solve problems involving right triangles.

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Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. *

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Define trigonometric ratios and solve problems involving right triangles.

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Derive and use the trigonometric ratios for special right triangles (30°, 60°, 90°and 45°, 45°, 90°). CA

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Represent and solve equations and inequalities graphically. [Combine polynomial, rational, radical, absolute value, and exponential functions.]

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Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. *

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Understand solving equations as a process of reasoning and explain the reasoning. [Simple radical and rational]

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Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

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Build a function that models a relationship between two quantities. [Include all types of functions studied.]

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Write a function that describes a relationship between two quantities. * Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. *