Gizmos for Georgia - Mathematics: Geometry (GA--Standards of Excellence adopted 2015)

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

MGSE9-12.G.CO: : Congruence

MGSE9-12.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.

MGSE9-12.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).

MGSE9-12.G.CO.4: : Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

MGSE9-12.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.

MGSE9-12.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.

MGSE9-12.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. (Extend to include HL and AAS.)

MGSE9-12.G.CO.9: : Prove theorems about lines and angles.

MGSE9-12.G.CO.10: : Prove theorems about triangles.

MGSE9-12.G.CO.11: : Prove theorems about parallelograms.

MGSE9-12.G.CO.13: : Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle.

MGSE9-12.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.

MGSE9-12.G.CO.10: : Prove theorems about triangles.

MGSE9-12.G.CO.11: : Prove theorems about parallelograms.

MGSE9-12.G.CO.13: : Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle.

MGSE9-12.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).

MGSE9-12.G.CO.4: : Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

MGSE9-12.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.

MGSE9-12.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.

MGSE9-12.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. (Extend to include HL and AAS.)

MGSE9-12.G.CO.9: : Prove theorems about lines and angles.

MGSE9-12.G.CO.10: : Prove theorems about triangles.

MGSE9-12.G.CO.11: : Prove theorems about parallelograms.

MGSE9-12.G.CO.13: : Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle.

MGSE9-12.G.SRT: : Similarity, Right Triangles, and Trigonometry

MGSE9-12.G.SRT.1a: : The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.

MGSE9-12.G.SRT.1b: : The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.

MGSE9-12.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.

MGSE9-12.G.SRT.4: : Prove theorems about triangles.

MGSE9-12.G.SRT.5: : Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

MGSE9-12.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.

MGSE9-12.G.SRT.8: : Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

MGSE9-12.G.SRT.1a: : The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.

MGSE9-12.G.SRT.1b: : The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.

MGSE9-12.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.

MGSE9-12.G.SRT.4: : Prove theorems about triangles.

MGSE9-12.G.SRT.5: : Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

MGSE9-12.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.

MGSE9-12.G.SRT.8: : Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

MGSE9-12.G.C: : Circles

MGSE9-12.G.CO.4: : Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

MGSE9-12.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. (Extend to include HL and AAS.)

MGSE9-12.G.CO.9: : Prove theorems about lines and angles.

MGSE9-12.G.CO.10: : Prove theorems about triangles.

MGSE9-12.G.CO.11: : Prove theorems about parallelograms.

MGSE9-12.G.CO.13: : Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle.

MGSE9-12.G.C.1: : Understand that all circles are similar.

MGSE9-12.G.C.2: : Identify and describe relationships among inscribed angles, radii, chords, tangents, and secants. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

MGSE9-12.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.

MGSE9-12.G.C.1: : Understand that all circles are similar.

MGSE9-12.G.C.2: : Identify and describe relationships among inscribed angles, radii, chords, tangents, and secants. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

MGSE9-12.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.

MGSE9-12.G.GPE: : Expressing Geometric Properties with Equations

MGSE9-12.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.

MGSE9-12.G.GPE.7: : Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

MGSE9-12.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.

MGSE9-12.G.GPE.7: : Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

MGSE9-12.G.GMD: : Geometric Measurement and Dimension

MGSE9-12.G.GMD.1a: : Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.

MGSE9-12.G.GMD.1b: : Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri’s principle.

MGSE9-12.G.GMD.3: : Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

MGSE9-12.G.GMD.1a: : Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.

MGSE9-12.G.GMD.1b: : Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri’s principle.

MGSE9-12.G.GMD.3: : Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

MGSE9-12.S.CP: : Conditional Probability and the Rules of Probability

MGSE9-12.S.CP.1: : Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events (or, and, not).

MGSE9-12.S.CP.2: : Understand that if two events A and B are independent, the probability of A and B occurring together is the product of their probabilities, and that if the probability of two events A and B occurring together is the product of their probabilities, the two events are independent.

MGSE9-12.S.CP.3: : Understand the conditional probability of A given B as P (A and B)/P(B). Interpret independence of A and B in terms of conditional probability; that is, 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.

MGSE9-12.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 context.

MGSE9-12.S.CP.1: : Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events (or, and, not).

MGSE9-12.S.CP.2: : Understand that if two events A and B are independent, the probability of A and B occurring together is the product of their probabilities, and that if the probability of two events A and B occurring together is the product of their probabilities, the two events are independent.

MGSE9-12.S.CP.3: : Understand the conditional probability of A given B as P (A and B)/P(B). Interpret independence of A and B in terms of conditional probability; that is, 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.

MGSE9-12.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 context.

Correlation last revised: 9/16/2020

Georgia - Mathematics: Geometry

GA--Standards of Excellence | Adopted: 2015

MGSE9-12.G.CO: : Congruence

MGSE9-12.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.

MGSE9-12.G.CO.4: : Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

MGSE9-12.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.

MGSE9-12.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.

MGSE9-12.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. (Extend to include HL and AAS.)

MGSE9-12.G.CO.9: : Prove theorems about lines and angles.

MGSE9-12.G.CO.10: : Prove theorems about triangles.

MGSE9-12.G.CO.11: : Prove theorems about parallelograms.

MGSE9-12.G.CO.13: : Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle.

MGSE9-12.G.SRT: : Similarity, Right Triangles, and Trigonometry

MGSE9-12.G.SRT.1a: : The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.

MGSE9-12.G.SRT.1b: : The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.

MGSE9-12.G.SRT.4: : Prove theorems about triangles.

MGSE9-12.G.SRT.5: : Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

MGSE9-12.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.

MGSE9-12.G.SRT.8: : Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

MGSE9-12.G.C: : Circles

MGSE9-12.G.C.1: : Understand that all circles are similar.

MGSE9-12.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.

MGSE9-12.G.GPE: : Expressing Geometric Properties with Equations

MGSE9-12.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.

MGSE9-12.G.GPE.7: : Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

MGSE9-12.G.GMD: : Geometric Measurement and Dimension

MGSE9-12.G.GMD.1a: : Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.

MGSE9-12.G.GMD.1b: : Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri’s principle.

MGSE9-12.G.GMD.3: : Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

MGSE9-12.S.CP: : Conditional Probability and the Rules of Probability

MGSE9-12.S.CP.1: : Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events (or, and, not).

MGSE9-12.S.CP.2: : Understand that if two events A and B are independent, the probability of A and B occurring together is the product of their probabilities, and that if the probability of two events A and B occurring together is the product of their probabilities, the two events are independent.

MGSE9-12.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 context.