### G: Geometry

#### G.CO: Congruence

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: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it 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 using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

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.

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

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.

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

G.SRT.14: Verify experimentally the properties of dilations given by a center and a scale factor:

G.SRT.14.a: 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.14.b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

G.SRT.15: 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.16: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

G.SRT.18: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

G.SRT.19: 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.20: Explain and use the relationship between the sine and cosine of complementary angles.

G.SRT.21: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

G.SRT.24: Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

#### G.C: Circles

G.C.25: Prove that all circles are similar.

G.C.26: Identify and describe relationships among inscribed angles, radii, and chords.

G.C.27: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

G.C.29: 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.

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

G.GPE.30: 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.

G.GPE.31: Use coordinates to prove simple geometric theorems algebraically.

G.GPE.32: Prove 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.33: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

G.GPE.34: 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

G.GMD.36: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

G.GMD.37: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

G.GMD.39: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

#### G.MG: Modeling with Geometry

G.MG.40: 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.41: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

### S: Statistics and Probability

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

S.CP.43: 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.44: 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.45: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

S.CP.46: 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.49: Use permutations and combinations to compute probabilities of compound events and solve problems.

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

S.MD.50: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

S.MD.51: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

Correlation last revised: 3/17/2015

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