Search the California Content Standards

Cluster:
Construct and compare linear, quadratic, and exponential models and solve problems. [Include quadratic.]

Standard:
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. *

Cluster:
Interpret expressions for functions in terms of the situation they model.

Standard:
Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity. CA *

Cluster:
Prove geometric theorems. [Focus on validity of underlying reasoning while using variety of ways of writing proofs.]

Standard:
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Cluster:
Prove geometric theorems. [Focus on validity of underlying reasoning while using variety of ways of writing proofs.]

Standard:
Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Cluster:
Prove geometric theorems. [Focus on validity of underlying reasoning while using variety of ways of writing proofs.]

Standard:
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

Cluster:
Understand similarity in terms of similarity transformations.

Standard:
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.

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

Standard:
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.