### G-CO: Congruence

#### 1.1: Experiment with transformations in the plane.

G-CO.1: State and apply precise definitions of angle, circle, perpendicular, parallel, ray, line segment, and distance based on the undefined notions of point, line, and plane.

G-CO.2: Represent transformations in the plane. (e.g., using transparencies and/or geometry software);

G-CO.2.a: Describe transformations as functions that take points in the plane as inputs and give other points as outputs.

G-CO.2.b: Compare transformations that preserve distance and angle to those that do not (e.g., translation versus dilation).

G-CO.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and/or reflections that map the figure onto itself.

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, (e.g., using graph paper, tracing paper, or geometry software). Specify a sequence of transformations that will map a given figure onto another.

#### 1.2: Understand congruence in terms of rigid motions.

G-CO.6: Use geometric descriptions of rigid motions to transform figures.

G-CO.6.a: Predict the effect of a given rigid motion on a given figure.

G-CO.6.b: Given two figures, use the definition of congruence in terms of rigid motions to decide if they 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.

#### 1.3: Prove geometric theorems.

G-CO.9: Prove theorems about lines and angles. Theorems must include but not limited to: vertical angles are congruent; when a transversal intersects parallel lines, alternate interior angles are congruent and same side interior angles are supplementary (using corresponding angles postulate); points on a perpendicular bisector of a line segment are equidistant from the segment's endpoints.

G-CO.11: Prove theorems about parallelograms. Theorems must include but not limited to: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

#### 1.4: Make geometric constructions.

G-CO.12: Perform geometric constructions with a compass and straightedge. including copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines/segments, constructing a line parallel to a given line through a point not on the line.

G-CO.13: Construct an equilateral triangle, a square, and a regular hexagon.

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

#### 2.1: Understand similarity in terms of similarity transformations.

G-SRT.1: Verify experimentally and apply the properties of dilations as determined by a center and a scale factor.

G-SRT.2: Determine whether figures are similar, using the definition of similarity and using similarity transformations.

G-SRT.3: Use the properties of similarity transformations to establish similarity theorems. Theorems must include AA, SAS, and SSS.

#### 2.2: Prove theorems involving similarity.

G-SRT.4: Prove theorems about triangles involving similarity. Theorems must include but not limited to: a line parallel to one side of a triangle divides the other two proportionally, and its converse; the Pythagorean Theorem proved using triangle similarity.

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

#### 2.3: Define trigonometric ratios and solve problems involving right triangles.

G-SRT.6: Define, using similarity, that side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios (sine, cosine, and tangent) for acute angles.

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

### G-C: Circles

#### 3.1: Understand and apply theorems about circles.

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

G-C.3: Construct, using a compass and straight edge, the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

#### 3.2: Find arc lengths and areas of sectors of circles.

G-C.5: Derive using similarity the length of the arc intercepted by an angle is proportional to the radius.

G-C.5.a: Define the radian measure of the angle as the constant of proportionality;

G-C.5.b: Derive and apply the formula for the area of a sector.

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

#### 4.1: 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.

#### 4.2: Use coordinates to prove simple geometric theorems algebraically.

G-GPE.5: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

### G-GMD: Geometric Measurement and Dimension

#### 5.1: Explain volume and surface area formulas and use them to solve problems.

G-GMD.1: Give an informal argument for the formulas for the volume of a cylinder, pyramid, sphere, and cone. Use dissection arguments, and informal limit arguments.

G-GMD.2: Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.

G-GMD.3: Know and apply volume and surface area formulas for cylinders, pyramids, cones, and spheres for composite figures to solve problems.

### S-CP: Statistics and Probability-Conditions Probability and Rules of Probability

#### 7.1: Understand independence and conditional probability and use them to interpret data.

S-CP.1: Describe events as subsets of a sample space or as unions, intersections, or complements of other events.

S-CP.2: Determine whether two events A and B are independent.

S-CP.3: Determine conditional probabilities and interpret independence by analyzing conditional probability.

S-CP.4: Construct and interpret two-way frequency tables of data. 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 situations.

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 result.

S-CP.8: Apply the general Multiplication Rule, P(A and B), and interpret the result.

Correlation last revised: 9/15/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.