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California High School Geometry Curriculum

Video lessons and practice for every high school Geometry topic. Aligned to California Common Core State Standards. Get help with proofs, transformations, and more.

California High School Geometry Curriculum | StudyPugHelp

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ID

Standard

StudyPug Topic

CA.G.G.CO.1

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

CA.G.G.CO.2

Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not.

CA.G.G.CO.4

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

CA.G.G.CO.6

Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

CA.G.G.CO.8

Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

CA.G.G.CO.10

Prove theorems about triangles.

CA.G.G.SRT.1

Verify experimentally the properties of dilations given by a center and a scale factor.

CA.G.G.SRT.2

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.

CA.G.G.SRT.6

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.

CA.G.G.SRT.8.1

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

CA.G.G.SRT.9

(+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

CA.G.G.SRT.10

(+) Prove the Laws of Sines and Cosines and use them to solve problems.

CA.G.G.SRT.11

(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.

CA.G.G.C.1

Prove that all circles are similar.

CA.G.G.C.2

Identify and describe relationships among inscribed angles, radii, and chords.

CA.G.G.C.3

Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

CA.G.G.C.5

Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians.

CA.G.G.GPE.1

Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

CA.G.G.GPE.2

Derive the equation of a parabola given a focus and directrix.

CA.G.G.GPE.5

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

CA.G.G.GPE.6

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

CA.G.G.GMD.1

Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

CA.G.G.GMD.3

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

CA.G.G.GMD.4

Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

CA.G.G.MG.3

Apply geometric methods to solve design problems.

CA.G.G.S.CP.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").

CA.G.G.S.CP.2

Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

CA.G.G.S.MD.6

(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

CA.G.G.S.MD.7

(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

California High School Geometry: What Students Learn

High school Geometry in California is built around the California Common Core State Standards. Students move from foundational definitions and transformations through to advanced topics like trigonometry, circle theorems, and probability. StudyPug covers every standard with clear video lessons and targeted practice problems.

Transformations and Congruence

Students begin by developing precise definitions of geometric figures and exploring transformations in the plane. Key skills include performing rotations, reflections, and translations, and using rigid motions to define congruence. Triangle congruence criteria — ASA, SAS, and SSS — are derived directly from these definitions, and students practice proving theorems about lines, angles, triangles, and parallelograms.

Similarity and Trigonometry

Building on transformations, students use similarity transformations to establish the AA criterion and prove relationships in geometric figures. Right triangle trigonometry introduces sine, cosine, and tangent ratios for acute angles, complementary angle relationships, and special right triangles (30-60-90 and 45-45-90). Students apply the Pythagorean Theorem and trigonometric ratios to solve real-world problems.

  • Understand side ratios in right triangles leading to trigonometric definitions
  • Use the relationship between sine and cosine of complementary angles
  • Apply Laws of Sines and Cosines to non-right triangles
  • Derive the area formula A = ½ab sin(C)

Circles and Analytic Geometry

Students prove that all circles are similar, identify relationships among inscribed angles, radii, and chords, and construct inscribed and circumscribed circles of triangles. Analytic geometry connects algebra and geometry: students derive the equations of circles and parabolas, use coordinates to prove geometric theorems, and apply the slope criteria for parallel and perpendicular lines.

Measurement, Modeling, and Probability

Later units cover volume formulas for cylinders, pyramids, cones, and spheres, and explore how scale factors affect length, area, and volume. Geometric modeling problems ask students to apply shapes and measurement to real design situations. The course concludes with probability, including conditional probability, independence, two-way frequency tables, and the Addition Rule.

  • Volume formulas for cylinders, pyramids, cones, and spheres
  • Cross-sections of 3D objects and solids of revolution
  • Conditional probability and the Addition Rule
  • Two-way frequency tables and independence

How StudyPug Supports California Geometry Students

Every StudyPug lesson is mapped to a specific California Common Core State Standards topic so students and parents can find exactly what they need. Whether it's a proof about parallelograms, a trig ratio problem, or a circle theorem, students can watch a short video lesson, replay it as many times as needed, and then practice with problems that match what their California teacher assigns.