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

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.