Learning Standards
OH.Math.HSG.CO.1: Know precise definitions of ray, angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and arc length.
Circles
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Inscribed Angles
Parallel, Intersecting, and Skew Lines
OH.Math.HSG.CO.2: 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
OH.Math.HSG.CO.3: Identify the symmetries of a figure, which are the rotations and reflections that carry it onto itself.
Dilations
Reflections
Rotations, Reflections, and Translations
Similar Figures
OH.Math.HSG.CO.3a: Identify figures that have line symmetry; draw and use lines of symmetry to analyze properties of shapes.
OH.Math.HSG.CO.3b: Identify figures that have rotational symmetry; determine the angle of rotation, and use rotational symmetry to analyze properties of shapes.
OH.Math.HSG.CO.4: 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
OH.Math.HSG.CO.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using items such as 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
OH.Math.HSG.CO.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 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
OH.Math.HSG.CO.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
OH.Math.HSG.CO.9: Prove and apply theorems about lines and angles.
1.3.1.1: Theorems include but are not restricted to the following: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
OH.Math.HSG.CO.10: Prove and apply theorems about triangles.
Isosceles and Equilateral Triangles
Polygon Angle Sum
Proving Triangles Congruent
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Triangle Angle Sum
Triangle Inequalities
1.3.2.1: Theorems include but are not restricted to the following: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Isosceles and Equilateral Triangles
Proving Triangles Congruent
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Triangle Angle Sum
Triangle Inequalities
OH.Math.HSG.CO.11: Prove and apply theorems about parallelograms.
Parallelogram Conditions
Special Parallelograms
1.3.3.1: Theorems include but are not restricted to the following: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
Parallelogram Conditions
Special Parallelograms
OH.Math.HSG.CO.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
1.4.1.1: Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors
OH.Math.HSG.CO.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Concurrent Lines, Medians, and Altitudes
Inscribed Angles
OH.Math.HSG.CO.14: Classify two-dimensional figures in a hierarchy based on properties.
Classifying Quadrilaterals
Classifying Triangles
Parallelogram Conditions
Special Parallelograms
OH.Math.HSG.SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor:
OH.Math.HSG.SRT.1a: 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.
OH.Math.HSG.SRT.1b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
OH.Math.HSG.SRT.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
Similarity in Right Triangles
OH.Math.HSG.SRT.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
OH.Math.HSG.SRT.4: Prove and apply theorems about triangles.
Congruence in Right Triangles
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Similar Figures
2.2.1.1: Theorems include but are not restricted to the following: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Similar Figures
OH.Math.HSG.SRT.5: Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures that can be decomposed into triangles.
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
OH.Math.HSG.SRT.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
OH.Math.HSG.SRT.8: Solve problems involving right triangles.
OH.Math.HSG.SRT.8a: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems if one of the two acute angles and a side length is given.
Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function
OH.Math.HSG.SRT.8b: 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
OH.Math.HSG.C.2: Identify and describe relationships among angles, radii, chords, tangents, and arcs and use them to solve problems.
Chords and Arcs
Circumference and Area of Circles
Inscribed Angles
3.1.2.1: Include the relationship between central, inscribed, and circumscribed angles and their intercepted arcs; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
Chords and Arcs
Circumference and Area of Circles
Inscribed Angles
OH.Math.HSG.C.3: Construct the inscribed and circumscribed circles of a triangle; prove and apply the property that opposite angles are supplementary for a quadrilateral inscribed in a circle.
Concurrent Lines, Medians, and Altitudes
Inscribed Angles
OH.Math.HSG.C.5: Find arc lengths and areas of sectors of circles.
OH.Math.HSG.C.5a: Apply similarity to relate the length of an arc intercepted by a central angle to the radius. Use the relationship to solve problems.
OH.Math.HSG.C.5b: Derive the formula for the area of a sector, and use it to solve problems.
OH.Math.HSG.C.6: Derive formulas that relate degrees and radians, and convert between the two.
Chords and Arcs
Cosine Function
Sine Function
Tangent Function
OH.Math.HSG.GPE.1: 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
OH.Math.HSG.GPE.2: Derive the equation of a parabola given a focus and directrix.
OH.Math.HSG.GPE.3: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
OH.Math.HSG.GPE.4: Use coordinates to prove simple geometric theorems algebraically and to verify geometric relationships algebraically, including properties of special triangles, quadrilaterals, and circles.
Circles
Cosine Function
Sine Function
Tangent Function
OH.Math.HSG.GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
OH.Math.HSG.GMD.1: 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
5.1.1.1: Use dissection arguments, Cavalieri's principle, and informal limit arguments.
Circumference and Area of Circles
Prisms and Cylinders
Pyramids and Cones
OH.Math.HSG.GMD.2: Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
Prisms and Cylinders
Pyramids and Cones
OH.Math.HSG.GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Prisms and Cylinders
Pyramids and Cones
OH.Math.HSG.GMD.6: When figures are similar, understand and apply the fact that when a figure is scaled by a factor of k, the effect on lengths, areas, and volumes is that they are multiplied by k, k², and k³, respectively.
Dilations
Perimeters and Areas of Similar Figures
Similar Figures
Correlation last revised: 9/15/2020