Course of Study
1.1.1: Experiment with transformations in the plane.
G-CO.1: Students will: 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.
Chords and Arcs
Circles
Circumference and Area of Circles
Classifying Quadrilaterals
Classifying Triangles
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Inscribed Angles
Investigating Angle Theorems
Parallel, Intersecting, and Skew Lines
Parallelogram Conditions
G-CO.2: Students will: 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
Reflections
Rotations, Reflections, and Translations
Translations
G-CO.3: Students will: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
Dilations
Reflections
Rotations, Reflections, and Translations
Similar Figures
G-CO.4: Students will: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
Circles
Dilations
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations
G-CO.5: Students will: 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.
Dilations
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations
1.1.2: Understand congruence in terms of rigid motions.
G-CO.6: Students will: 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
Proving Triangles Congruent
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations
G-CO.7: Students will: 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.
Reflections
Rotations, Reflections, and Translations
Translations
G-CO.8: Students will: Explain how the criteria for triangle congruence, angle-side-angle (ASA), side-angle-side (SAS), and side-side-side (SSS), follow from the definition of congruence in terms of rigid motions.
1.1.3: Prove geometric theorems.
G-CO.9: Students will: Prove theorems about lines and angles.
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Investigating Angle Theorems
Parallel, Intersecting, and Skew Lines
G-CO.10: Students will: Prove theorems about triangles.
Concurrent Lines, Medians, and Altitudes
Congruence in Right Triangles
Investigating Angle Theorems
Isosceles and Equilateral Triangles
Proving Triangles Congruent
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Segment and Angle Bisectors
Triangle Angle Sum
Triangle Inequalities
G-CO.11: Students will: Prove theorems about parallelograms.
Classifying Quadrilaterals
Parallelogram Conditions
Special Parallelograms
1.1.4: Make geometric constructions.
G-CO.12: Students will: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software.
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors
G-CO.13: Students will: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Concurrent Lines, Medians, and Altitudes
Inscribed Angles
1.2.1: Understand similarity in terms of similarity transformations.
G-SRT.14: Students will: 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: Students will: 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
Similarity in Right Triangles
G-SRT.16: Students will: Use the properties of similarity transformations to establish the angle-angle (AA) criterion for two triangles to be similar.
1.2.2: Prove theorems involving similarity.
G-SRT.17: Students will: Prove theorems about triangles.
Proving Triangles Congruent
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Similar Figures
G-SRT.18: Students will: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Chords and Arcs
Congruence in Right Triangles
Constructing Congruent Segments and Angles
Dilations
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures
Similarity in Right Triangles
1.2.3: Define trigonometric ratios and solve problems involving right triangles.
G-SRT.19: Students will: 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.20: Students will: Explain and use the relationship between the sine and cosine of complementary angles.
Sine, Cosine, and Tangent Ratios
G-SRT.21: Students will: 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
1.3.1: Understand and apply theorems about circles.
G-C.24: Students will: Prove that all circles are similar.
G-C.25: Students will: Identify and describe relationships among inscribed angles, radii, and chords.
Chords and Arcs
Circumference and Area of Circles
Inscribed Angles
G-C.26: Students will: 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
1.3.2: Find arc lengths and areas of sectors of circles.
G-C.28: Students will: 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.
1.4.1: Translate between the geometric description and the equation for a conic section.
G-GPE.29: Students will: 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
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
1.4.2: Use coordinates to prove simple geometric theorems algebraically.
G-GPE.31: Students will: 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).
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
G-GPE.33: Students will: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
1.4.3: Use coordinates to prove simple geometric theorems algebraically.
G-GPE.34: Students will: Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics.
1.5.1: Explain volume formulas and use them to solve problems.
G-GMD.35: Students will: Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone.
Circumference and Area of Circles
Prisms and Cylinders
Pyramids and Cones
G-GMD.36: Students will: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Prisms and Cylinders
Pyramids and Cones
G-GMD.37: Students will: Determine the relationship between surface areas of similar figures and volumes of similar figures.
Surface and Lateral Areas of Prisms and Cylinders
1.5.2: Visualize relationships between two-dimensional and three-dimensional objects.
G-GMD.38: Students will: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
1.6.1: Apply geometric concepts in modeling situations.
G-MG.39: Students will: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
Prisms and Cylinders
Pyramids and Cones
G-MG.40: Students will: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, British Thermal Units (BTUs) per cubic foot).
Density
Density Experiment: Slice and Dice
Density Laboratory
G-MG.41: Students will: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).
2.1.1: Use probability to evaluate outcomes of decisions.
S-MD.42: Students will: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
Lucky Duck (Expected Value)
Probability Simulations
Theoretical and Experimental Probability
S-MD.43: Students will: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
Estimating Population Size
Lucky Duck (Expected Value)
Probability Simulations
Theoretical and Experimental Probability
Correlation last revised: 9/15/2020