### G-CO: Congruence

#### 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.

Circles

Constructing Congruent Segments and Angles

Constructing Parallel and Perpendicular Lines

#### 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).

Dilations

Reflections

Rotations, Reflections, and Translations

Translations

#### G-CO.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

Dilations

Reflections

Rotations, Reflections, and Translations

Translations

#### G-CO.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

Dilations

Reflections

Rotations, Reflections, and Translations

Translations

#### 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.

Proving Triangles Congruent

Reflections

Rotations, Reflections, and Translations

Translations

#### 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.

Proving Triangles Congruent

#### G-CO.9: Prove theorems about lines and angles.

Investigating Angle Theorems

#### G-CO.10: Prove theorems about triangles.

Pythagorean Theorem

Triangle Angle Sum

Triangle Inequalities

#### G-CO.11: Prove theorems about parallelograms.

Parallelogram Conditions

Special Parallelograms

#### 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.).

Constructing Congruent Segments and Angles

Constructing Parallel and Perpendicular Lines

### G-SRT: Similarity, Right Triangles, and Trigonometry

#### G-SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor:

G-SRT.1.b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

Dilations

Similar Figures

#### 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.

Similar Figures

#### G-SRT.4: Prove theorems about triangles.

Pythagorean Theorem

Similar Figures

#### G-SRT.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Dilations

Perimeters and Areas of Similar Figures

Similarity in 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.

Sine, Cosine, and Tangent Ratios

#### G-SRT.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Cosine Function

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Sine Function

Sine, Cosine, and Tangent Ratios

Tangent Function

G-SRT.8.1: Derive and use the trigonometric ratios for special right triangles (30°,60°,90°and 45°,45°,90°).

Cosine Function

Sine Function

Tangent Function

### G-C: Circles

#### G-C.2: Identify and describe relationships among inscribed angles, radii, and chords.

Inscribed Angles

#### 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.

Chords and Arcs

### G-GPE: Expressing Geometric Properties with Equations

#### 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.

Circles

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

#### G-GPE.2: Derive the equation of a parabola given a focus and directrix.

Parabolas

#### G-GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

Distance Formula

### G-GMD: Geometric Measurement and Dimension

#### 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.

Circumference and Area of Circles

Prisms and Cylinders

Pyramids and Cones

#### G-GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Prisms and Cylinders

Pyramids and Cones

#### G-GMD.5: Know that the effect of a scale factor k greater than zero on length, area, and volume is to multiply each by k, k², and k³, respectively; determine length, area and volume measures using scale factors.

Dilations

### S-CP: Conditional Probability and the Rules of Probability

#### 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').

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

#### 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.

Independent and Dependent Events

#### 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.

Independent and Dependent Events

#### S-CP.9: Use permutations and combinations to compute probabilities of compound events and solve problems.

Binomial Probabilities

Permutations and Combinations

### S-MD: Using Probability to Make Decisions

#### S-MD.6: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

Lucky Duck (Expected Value)

#### 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).

Lucky Duck (Expected Value)

Correlation last revised: 9/16/2020