Search the California Content Standards

Cluster:
Create equations that describe numbers or relationships.

Standard:
Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. CA *

Cluster:
Create equations that describe numbers or relationships.

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Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. *

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Create equations that describe numbers or relationships.

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Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. * [Include formulas involving quadratic terms.]

Cluster:
Understand similarity in terms of similarity transformations.

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Verify experimentally the properties of dilations given by a center and a scale factor: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

Cluster:
Understand similarity in terms of similarity transformations.

Standard:
Verify experimentally the properties of dilations given by a center and a scale factor: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

Cluster:
Understand similarity in terms of similarity transformations.

Standard:
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Cluster:
Understand similarity in terms of similarity transformations.

Standard:
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.

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

Standard:
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.

Standard:
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.