G-CO: Congruence

1.1: Experiment with transformations in the plane

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
 Inscribed Angles
 Parallel, Intersecting, and Skew 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
 Rotations, Reflections, and Translations
 Translations

G-CO.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it on to itself.

 Reflections
 Rotations, Reflections, and Translations
 Similar Figures

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

 Circles
 Rotations, Reflections, and Translations
 Similar Figures
 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 on to another.

 Reflections
 Rotations, Reflections, and Translations
 Similar Figures
 Translations

1.2: 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.

 Absolute Value with Linear Functions
 Circles
 Dilations
 Holiday Snowflake Designer
 Reflections
 Rotations, Reflections, and Translations
 Similar Figures
 Translations

1.3: Prove geometric theorems

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

 Investigating Angle Theorems

G-CO.10: Prove theorems about triangles.

 Isosceles and Equilateral Triangles
 Triangle Angle Sum
 Triangle Inequalities

G-CO.11: Prove theorems about parallelograms.

 Parallelogram Conditions
 Special Parallelograms

1.4: Make geometric constructions

G-CO.12: Make formal geometric constructions with a variety of tools and methods (compass and straight edge, string, reflective devices, paper folding, dynamic geometric software, etc.).

 Constructing Congruent Segments and Angles
 Constructing Parallel and Perpendicular Lines
 Segment and Angle Bisectors

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

 Concurrent Lines, Medians, and Altitudes
 Inscribed Angles

G-SRT: Similarity, Right Triangles, and Trigonometry

2.1: 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.1.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.

 Dilations

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.

 Circles
 Dilations
 Similar Figures

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

 Similar Figures

2.2: Prove theorems involving similarity

G-SRT.4: Prove theorems about triangles.

 Similar Figures

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

 Congruence in Right Triangles
 Constructing Congruent Segments and Angles
 Perimeters and Areas of Similar Figures
 Proving Triangles Congruent
 Similar Figures
 Similarity in Right Triangles

2.3: 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.

 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-C: Circles

3.1: Understand and apply theorems about circles

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

 Chords and Arcs
 Circumference and Area of Circles
 Inscribed Angles

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

 Concurrent Lines, Medians, and Altitudes
 Inscribed Angles

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.

 Circles

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

 Parabolas

G-GPE.3: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

 Ellipses
 Hyperbolas

G-GMD: Geometric Measurement and Dimension

5.1: 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, volume of a cylinder, pyramid, and cone.

 Circumference and Area of Circles
 Prisms and Cylinders
 Pyramids and Cones

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

 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

Correlation last revised: 4/4/2018

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