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