Content Standards
HS.G-CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, and plane.
Circles
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Inscribed Angles
Parallel, Intersecting, and Skew Lines
HS.G-CO.2.i: Represent transformations in the plane.
Dilations
Reflections
Rotations, Reflections, and Translations
Translations
HS.G-CO.2.ii: Describe transformations as functions that take points in the plane as inputs and give other points as outputs.
Dilations
Reflections
Rotations, Reflections, and Translations
Translations
HS.G-CO.2.iii: 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
HS.G-CO.3: 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
HS.G-CO.4: Develop or verify experimentally the characteristics 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
HS.G-CO.5.i: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software.
Dilations
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations
HS.G-CO.5.ii: Specify a sequence of transformations that will carry a given figure onto another.
Dilations
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations
HS.G-CO.6.i: Use geometric descriptions of rigid motions to predict the effect of a given rigid motion on a given figure.
Absolute Value with Linear Functions
Circles
Dilations
Holiday Snowflake Designer
Proving Triangles Congruent
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations
HS.G-CO.6.ii: Use the definition of congruence in terms of rigid motions to decide if two figures are congruent.
Absolute Value with Linear Functions
Circles
Dilations
Holiday Snowflake Designer
Proving Triangles Congruent
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations
HS.G-CO.8: Prove two triangles are congruent using the congruence theorems such as ASA, SAS, and SSS.
Congruence in Right Triangles
Proving Triangles Congruent
HS.G-CO.9: Prove and apply theorems about lines and angles.
Investigating Angle Theorems
Slope
HS.G-CO.10: Prove and apply theorems about triangle properties.
Isosceles and Equilateral Triangles
Polygon Angle Sum
Proving Triangles Congruent
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Triangle Angle Sum
Triangle Inequalities
HS.G-CO.11: Prove and apply theorems about parallelograms.
Parallelogram Conditions
Special Parallelograms
HS.G-CO.12: Make basic geometric constructions with a variety of tools and methods.
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors
1.4.1.2: Tools may include compass and straightedge, string, reflective devices, paper folding or dynamic geometric software.
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors
HS.G-CO.13: Apply basic constructions to create polygons such as equilateral triangles, squares, and regular hexagons inscribed in circles.
Concurrent Lines, Medians, and Altitudes
Inscribed Angles
HS.G-SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor.
HS.G-SRT.2.i: Given two figures, use transformations to decide if they are similar.
Circles
Dilations
Similar Figures
Similarity in Right Triangles
HS.G-SRT.2.ii: Apply 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
HS.G-SRT.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
HS.G-SRT.4: Prove similarity theorems about triangles.
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Similar Figures
HS.G-SRT.5: 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
HS.G-SRT.6: Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine, and tangent of an acute angle in a right triangle.
Sine, Cosine, and Tangent Ratios
HS.G-SRT.8: Use special right triangles (30°-60°-90° and 45°-45°-90°), 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
HS.G-C.1: Understand and apply theorems about relationships with line segments and circles including radii, diameter, secants, tangents, and chords.
Chords and Arcs
Circumference and Area of Circles
Inscribed Angles
HS.G-C.2.i: Understand and apply theorems about relationships with angles formed by radii, diameter, secants, tangents, and chords.
Chords and Arcs
Circumference and Area of Circles
Inscribed Angles
HS.G-C.2.ii: Understand and apply properties of angles for a quadrilateral inscribed in a circle.
Concurrent Lines, Medians, and Altitudes
Inscribed Angles
HS.G-C.3: Construct the incenter and circumcenter of a triangle. Relate the incenter and circumcenter to the inscribed and circumscribed circles.
Concurrent Lines, Medians, and Altitudes
HS.G-C.5: Explain and use the formulas for arc length and area of sectors of circles.
HS.G-GPE.1.i: Derive the equation of a circle of given center and radius.
Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
HS.G-GPE.1.ii: Derive the equation of a parabola given a focus and directrix.
HS.G-GPE.1.iii: Derive the equations of ellipses and hyperbolas given foci, using the fact that the sum or difference of distances from the foci is constant.
HS.G-GPE.3.i: Identify key features of conic sections given their equations.
Addition and Subtraction of Functions
Circles
Ellipses
Hyperbolas
Parabolas
HS.G-GPE.3.ii: Apply properties of conic sections in real world situations.
HS.G-GPE.5.i: Develop and verify the slope criteria for parallel and perpendicular lines.
Cat and Mouse (Modeling with Linear Systems)
HS.G-GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles, parallelograms, trapezoids and kites.
HS.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
5.1.1.1: May use dissection arguments. Cavalieri’s Principle or informal limit arguments.
5.1.1.2: Cavalieri’s Principle: 2D: Suppose two regions in a plane are included between two parallel lines in that plane. If every line parallel to these two lines intersects both regions in line segments of equal length, then the two regions have equal areas.
HS.G-GMD.2: Calculate the surface area for prisms, cylinders, pyramids, cones, and spheres to solve problems.
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones
HS.G-GMD.3: Know and apply volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems.
Prisms and Cylinders
Pyramids and Cones
Correlation last revised: 9/22/2020