G: Geometry

G.CO: Congruence

G.CO.A: Experiment with transformations in the plane.

G.CO.A.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, plane, distance along a line, and distance around a circular arc.

Circles
Inscribed Angles
Parallel, Intersecting, and Skew Lines

G.CO.A.2: Represent transformations in the plane in multiple ways, including technology. Describe transformations as functions that take points in the plane (pre-image) as inputs and give other points (image) as outputs. Compare transformations that preserve distance and angle measure to those that do not (e.g., translation versus horizontal stretch).

Dilations
Rotations, Reflections, and Translations
Translations

G.CO.A.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry the shape onto itself.

Reflections
Rotations, Reflections, and Translations
Similar Figures

G.CO.A.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.A.5: Given a geometric figure and a rigid motion, draw the image of the figure in multiple ways, including technology. Specify a sequence of rigid motions that will carry a given figure onto another.

Dilations
Reflections
Rotations, Reflections, and Translations
Translations

G.CO.B: Understand congruence in terms of rigid motions.

G.CO.B.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 determine informally if they are congruent.

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

G.CO.C: Prove geometric theorems.

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

Investigating Angle Theorems

G.CO.C.10: Prove theorems about triangles.

Isosceles and Equilateral Triangles
Triangle Angle Sum
Triangle Inequalities

G.CO.C.11: Prove theorems about parallelograms.

Parallelogram Conditions
Special Parallelograms

G.CO.D: Make geometric constructions.

G.CO.D.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
Segment and Angle Bisectors

G.SRT: Similarity, Right Triangles, and Trigonometry

G.SRT.A: Understand similarity in terms of similarity transformations.

G.SRT.A.1: Verify informally the properties of dilations given by a center and a scale factor.

Dilations
Similar Figures

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

Similar Figures

G.SRT.B: Prove theorems involving similarity.

G.SRT.B.4: Prove theorems about similar triangles.

Similar Figures

G.SRT.B.5: Use congruence and similarity criteria for triangles to solve problems and to justify 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

G.SRT.C: Define trigonometric ratios and solve problems involving triangles.

G.SRT.C.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.C.8: Solve triangles.

G.SRT.C.8.a: Know and 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

G.C.A: Understand and apply theorems about circles.

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

Chords and Arcs
Circumference and Area of Circles
Inscribed Angles

G.C.A.3: Construct the incenter and circumcenter of a triangle and use their properties to solve problems in context.

Concurrent Lines, Medians, and Altitudes

G.GPE: Expressing Geometric Properties with Equations

G.GPE.A: Translate between the geometric description and the equation for a circle.

G.GPE.A.1: Know and write the equation of a circle of given center and radius using the Pythagorean Theorem.

Circles

G.GMD: Geometric Measurement and Dimension

G.GMD.A: Explain volume and surface area formulas and use them to solve problems.

G.GMD.A.1: Give an informal argument for the formulas for the circumference of a circle and the volume and surface area of a cylinder, cone, prism, and pyramid.

Circumference and Area of Circles
Prisms and Cylinders
Pyramids and Cones

G.GMD.A.2: Know and use volume and surface area formulas for cylinders, cones, prisms, pyramids, and spheres to solve problems.

Prisms and Cylinders
Pyramids and Cones