## Description

- Overview:
- The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards. Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

- Remix of:
- OREGON MATH STANDARDS (2021): [TEMPLATE]
- Subject:
- Mathematics
- Level:
- High School
- Material Type:
- Teaching/Learning Strategy
- Author:
- Mark Freed
- Date Added:
- 07/11/2023

- License:
- Creative Commons Attribution
- Language:
- English

## Standards

Learning Domain: Geometry: Congruence

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Congruence

Standard: 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).

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Congruence

Standard: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Congruence

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Congruence

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Congruence

Standard: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Congruence

Standard: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Congruence

Standard: Prove theorems about lines and angles. Theorems include: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Congruence

Standard: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Geometric Measurement and Dimension

Standard: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Geometric Measurement and Dimension

Standard: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Expressing Geometric Properties with Equations

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Expressing Geometric Properties with Equations

Standard: Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, ‰ö_3) lies on the circle centered at the origin and containing the point (0, 2).

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Expressing Geometric Properties with Equations

Standard: 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).

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Modeling with Geometry

Standard: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Modeling with Geometry

Standard: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Modeling with Geometry

Standard: 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).*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Similarity, Right Triangles, and Trigonometry

Standard: Verify experimentally the properties of dilations given by a center and a scale factor:

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Similarity, Right Triangles, and Trigonometry

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Similarity, Right Triangles, and Trigonometry

Standard: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Similarity, Right Triangles, and Trigonometry

Standard: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Similarity, Right Triangles, and Trigonometry

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Similarity, Right Triangles, and Trigonometry

Standard: Explain and use the relationship between the sine and cosine of complementary angles.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Similarity, Right Triangles, and Trigonometry

Standard: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Degree of Alignment: Not Rated (0 users)

Cluster: Experiment with transformations in the plane

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Experiment with transformations in the plane

Standard: 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).

Degree of Alignment: Not Rated (0 users)

Cluster: Experiment with transformations in the plane

Standard: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

Degree of Alignment: Not Rated (0 users)

Cluster: Experiment with transformations in the plane

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Understand congruence in terms of rigid motions

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Understand congruence in terms of rigid motions

Standard: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Degree of Alignment: Not Rated (0 users)

Cluster: Prove geometric theorems

Standard: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Prove geometric theorems

Standard: Prove theorems about lines and angles. Theorems include: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Make geometric constructions

Standard: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Understand similarity in terms of similarity transformations

Standard: Verify experimentally the properties of dilations given by a center and a scale factor:

Degree of Alignment: Not Rated (0 users)

Cluster: Understand similarity in terms of similarity transformations

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Understand similarity in terms of similarity transformations

Standard: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Degree of Alignment: Not Rated (0 users)

Cluster: Prove theorems involving similarity

Standard: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Degree of Alignment: Not Rated (0 users)

Cluster: Define trigonometric ratios and solve problems involving right triangles

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Define trigonometric ratios and solve problems involving right triangles

Standard: Explain and use the relationship between the sine and cosine of complementary angles.

Degree of Alignment: Not Rated (0 users)

Cluster: Define trigonometric ratios and solve problems involving right triangles

Standard: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Degree of Alignment: Not Rated (0 users)

Cluster: Translate between the geometric description and the equation for a conic section

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Use coordinates to prove simple geometric theorems algebraically

Standard: Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

Degree of Alignment: Not Rated (0 users)

Cluster: Use coordinates to prove simple geometric theorems algebraically

Standard: 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).

Degree of Alignment: Not Rated (0 users)

Cluster: Explain volume formulas and use them to solve problems

Standard: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

Degree of Alignment: Not Rated (0 users)

Cluster: Explain volume formulas and use them to solve problems

Standard: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*

Degree of Alignment: Not Rated (0 users)

Cluster: Apply geometric concepts in modeling situations

Standard: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*

Degree of Alignment: Not Rated (0 users)

Cluster: Apply geometric concepts in modeling situations

Standard: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).*

Degree of Alignment: Not Rated (0 users)

Cluster: Apply geometric concepts in modeling situations

Standard: 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).*

Degree of Alignment: Not Rated (0 users)

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