- standard
Understand similarity in terms of similarity transformations
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Similarity, Right Triangles, and Trigonometry
Verify experimentally the properties of dilations given by a center and a scale factor:
- standard
Make geometric constructions
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Congruence
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
- standard
Make geometric constructions
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Congruence
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric…
- standard
Prove geometric theorems
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Congruence
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles ar…
- standard
Prove geometric theorems
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Congruence
Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect eac…
- standard
Prove geometric theorems
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Congruence
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruen…
- standard
Understand congruence in terms of rigid motions
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Congruence
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
- standard
Understand congruence in terms of rigid motions
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Congruence
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 correspondi…
- standard
Understand congruence in terms of rigid motions
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Congruence
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 th…
- standard
Experiment with transformations in the plane
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Congruence
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software.…
- standard
Experiment with transformations in the plane
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Congruence
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
- standard
Experiment with transformations in the plane
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Congruence
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
- standard
Experiment with transformations in the plane
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Congruence
Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane a…
- standard
Experiment with transformations in the plane
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Congruence
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a…