Academic Standards
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.
Chords and Arcs
Constructing Parallel and Perpendicular Lines
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
Reflections
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
G.CO.A.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
Reflections
Rotations, Reflections, and Translations
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.
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.
Reflections
Rotations, Reflections, and Translations
Translations
G.CO.C: Prove geometric theorems.
G.CO.C.9: Prove theorems about lines and angles.
Constructing Parallel and Perpendicular Lines
Investigating Angle Theorems
Segment and Angle Bisectors
G.CO.C.10: Prove theorems about triangles.
Concurrent Lines, Medians, and Altitudes
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.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.
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.
G.SRT.A.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
G.SRT.B: Prove theorems involving similarity.
G.SRT.B.4: Prove theorems about similar triangles.
Similar Figures
Similarity in Right Triangles
G.SRT.B.5: Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures.
Chords and Arcs
Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Pythagorean Theorem
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.7: Explain and use the relationship between the sine and cosine of complementary angles.
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.
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine, Cosine, and Tangent Ratios
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
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.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.
G.GPE.B: Use coordinates to prove simple geometric theorems algebraically.
G.GPE.B.5: Know and use coordinates to compute perimeters of polygons and areas of triangles and rectangles.
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
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of 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.
Measuring Volume
Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones
G.MG.A: Apply geometric concepts in modeling situations.
G.MG.A.2: Apply geometric methods to solve real-world problems.
3D and Orthographic Views
Geometric Probability
Correlation last revised: 2/1/2022