Looking for free content that’s aligned to your standards? You’ve come to the right place!

## Get Free Geometry Math Content

Khan Academy is a nonprofit with thousands of free videos, articles, and practice questions for just about every standard.

No ads, no subscriptions – just 100% free, forever.

### G Geometry

- G.CO Congruence
- Experiment with transformations in the plane.
- G.CO.1 Know precise definitions of ray, angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and arc length.
- 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, e.g., translation versus horizontal stretch.
- G.CO.3 Identify the symmetries of a figure, which are the rotations and reflections that carry it onto itself.
- G.CO.3a Identify figures that have line symmetry; draw and use lines of symmetry to analyze properties of shapes.
- G.CO.3b Identify figures that have rotational symmetry; determine the angle of rotation, and use rotational symmetry to analyze properties of shapes.

- G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
- G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using items such as graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
- Checkpoint opportunity

- Understand congruence in terms of rigid motions.
- 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.
- G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
- 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.
- Checkpoint opportunity

- Prove geometric theorems both formally and informally using a variety of methods.
- G.CO.9 Prove and apply theorems about lines and angles.
- G.CO.10 Prove and apply theorems about triangles.
- G.CO.11 Prove and apply theorems about parallelograms.
- Checkpoint opportunity

- Make geometric constructions.
- G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
- G.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
- Checkpoint opportunity

- Classify and analyze geometric figures.
- G.CO.14 Classify two-dimensional figures in a hierarchy based on properties.

- Experiment with transformations in the plane.
- G.SRT Similarity, Right Triangles, and Trigonometry
- Understand similarity in terms of similarity transformations.
- G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor:
- G.SRT.1a 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.
- G.SRT.1b The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

- 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.
- G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
- Checkpoint opportunity

- G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor:
- Prove and apply theorems both formally and informally involving similarity using a variety of methods.
- G.SRT.4 Prove and apply theorems about triangles.
- G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures that can be decomposed into triangles.
- Checkpoint opportunity

- Define trigonometric ratios, and solve problems involving right triangles.
- 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.
- G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
- G.SRT.8 Solve problems involving right triangles.
- G.SRT.8a Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems if one of the two acute angles and a side length is given.
- G.SRT.8b Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

- Checkpoint opportunity

- Understand similarity in terms of similarity transformations.
- G.C Circles
- Understand and apply theorems about circles.
- G.C.1 Prove that all circles are similar using transformational arguments.
- G.C.2 Identify and describe relationships among angles, radii, chords, tangents, and arcs and use them to solve problems.
- G.C.3 Construct the inscribed and circumscribed circles of a triangle; prove and apply the property that opposite angles are supplementary for a quadrilateral inscribed in a circle.
- G.C.4 Construct a tangent line from a point outside a given circle to the circle.
- Checkpoint opportunity

- Find arc lengths and areas of sectors of circles.
- G.C.5 Find arc lengths and areas of sectors of circles.
- G.C.5a Apply similarity to relate the length of an arc intercepted by a central angle to the radius. Use the relationship to solve problems.
- G.C.5b Derive the formula for the area of a sector, and use it to solve problems.

- Checkpoint opportunity

- G.C.5 Find arc lengths and areas of sectors of circles.

- Understand and apply theorems about circles.
- G.GPE Expressing Geometric Properties with Equations
- Translate between the geometric description and the equation for a conic section.
- 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.
- Checkpoint opportunity

- Use coordinates to prove simple geometric theorems algebraically and to verify specific geometric statements.
- G.GPE.4 Use coordinates to prove simple geometric theorems algebraically and to verify geometric relationships algebraically, including properties of special triangles, quadrilaterals, and circles.
- G.GPE.5 Justify the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems, e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point.
- G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
- G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
- Checkpoint opportunity

- Translate between the geometric description and the equation for a conic section.
- G.GMD Geometric Measurement and Dimension
- Explain volume formulas, and use them to solve problems.
- G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone.
- G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
- Checkpoint opportunity

- Visualize relationships between two-dimensional and three-dimensional objects.
- 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.
- Checkpoint opportunity

- Understand the relationships between lengths, area, and volumes.
- G.GMD.5 Understand how and when changes to the measures of a figure (lengths or angles) result in similar and non-similar figures.
- G.GMD.6 When figures are similar, understand and apply the fact that when a figure is scaled by a factor of
*k*, the effect on lengths, areas, and volumes is that they are multiplied by*k*,*k*², and*k*³, respectively.

- Explain volume formulas, and use them to solve problems.
- G.MG Modeling with Geometry
- Apply geometric concepts in modeling situations.
- G.MG.1 Use geometric shapes, their measures, and their properties to describe objects, e.g., modeling a tree trunk or a human torso as a cylinder.
- G.MG.2 Apply concepts of density based on area and volume in modeling situations, e.g., persons per square mile, BTUs per cubic foot.
- G.MG.3 Apply geometric methods to solve design problems, e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios.
- Checkpoint opportunity

- Apply geometric concepts in modeling situations.

### S Statistics and Probability

- S.CP Conditional Probability and the Rules of Probability
- Understand independence and conditional probability, and use them to interpret data.
- 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”).
- S.CP.2 Understand that two events A and B are independent if and only 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.
- S.CP.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
- S.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
- S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

- Use the rules of probability to compute probabilities of compound events in a uniform probability model.
- S.CP.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.
- S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.
- S.CP.8 Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)·P(B|A) = P(B)·P(A|B), and interpret the answer in terms of the model.
- S.CP.9 Use permutations and combinations to compute probabilities of compound events and solve problems.
- Checkpoint opportunity

- Understand independence and conditional probability, and use them to interpret data.