- standard
Visualize relationships between two-dimensional and three-dimensional objects
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Geometric Measurement and Dimension
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimens…
- standard
Explain volume formulas and use them to solve problems
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Geometric Measurement and Dimension
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*
- standard
Explain volume formulas and use them to solve problems
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Geometric Measurement and Dimension
(+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
- standard
Explain volume formulas and use them to solve problems
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Geometric Measurement and Dimension
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 argumen…
- standard
Use coordinates to prove simple geometric theorems algebraically
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Expressing Geometric Properties with Equations
Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g.…
- standard
Use coordinates to prove simple geometric theorems algebraically
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Expressing Geometric Properties with Equations
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
- standard
Use coordinates to prove simple geometric theorems algebraically
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Expressing Geometric Properties with Equations
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 perpendic…
- standard
Use coordinates to prove simple geometric theorems algebraically
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Expressing Geometric Properties with Equations
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate p…
- standard
Translate between the geometric description and the equation for a conic section
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Expressing Geometric Properties with Equations
(+) 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.
- standard
Translate between the geometric description and the equation for a conic section
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Expressing Geometric Properties with Equations
Derive the equation of a parabola given a focus and directrix.
- standard
Translate between the geometric description and the equation for a conic section
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Expressing Geometric Properties with Equations
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 b…
- standard
Find arc lengths and areas of sectors of circles
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Circles
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle a…
- standard
Understand and apply theorems about circles
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Circles
Construct a tangent line from a point outside a given circle to the circle.
- standard
Understand and apply theorems about circles
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Circles
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.