Search the California Content Standards

Cluster:
Understand congruence and similarity using physical models, transparencies, or geometry software.

Standard:
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

Cluster:
Understand congruence and similarity using physical models, transparencies, or geometry software.

Standard:
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Cluster:
Understand congruence and similarity using physical models, transparencies, or geometry software.

Standard:
Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Cluster:
Understand congruence and similarity using physical models, transparencies, or geometry software.

Standard:
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Cluster:
Understand and apply the Pythagorean Theorem.

Standard:
Explain a proof of the Pythagorean Theorem and its converse.

Cluster:
Understand and apply the Pythagorean Theorem.

Standard:
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Cluster:
Understand and apply the Pythagorean Theorem.

Standard:
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Cluster:
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Standard:
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Cluster:
Solve equations and inequalities in one variable. [Quadratics with real coefficients]

Standard:
Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form.

Cluster:
Solve equations and inequalities in one variable. [Quadratics with real coefficients]

Standard:
Solve quadratic equations in one variable. Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.