## Status message

Dear LOR user,

Thank you for being a big part of this community. To better support the initiatives around open educational resources in the state of Michigan, all resources on the Michigan Virtual Learning Object Repository (LOR) are being moved to #GoOpen Michigan (link is external) on September 30th, 2018. During the transition, our LOR will be moved to an archived state, not allowing new user registration or new content to be added. An email with more details was sent to registered users of the LOR in September. To make use of the great resources on the platform, we encourage you to create an account and add your own new resources to the #GoOpen Michigan platform (link is external).

# Standards: Math

(0)
Translate between the geometric description and the equation for a conic section.
Education Level: 9-12
Description:

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.

(0)
Translate between the geometric description and the equation for a conic section.
Education Level: 9-12
Description:

Derive the equation of a parabola given a focus and directrix.

(0)
Translate between the geometric description and the equation for a conic section.
Education Level: 9-12
Description:

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.

(0)
Use coordinates to prove simple geometric theorems algebraically.
Education Level: 9-12
Description:

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).

(0)
Use coordinates to prove simple geometric theorems algebraically.
Education Level: 9-12
Description:

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).

(0)
Use coordinates to prove simple geometric theorems algebraically.
Education Level: 9-12
Description:

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

(0)
Use coordinates to prove simple geometric theorems algebraically.
Education Level: 9-12
Description:

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*

(0)
Apply geometric concepts in modeling situations.
Education Level: 9-12
Description:

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

(0)
Apply geometric concepts in modeling situations.
Education Level: 9-12
Description:

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

(0)
Apply geometric concepts in modeling situations.
Education Level: 9-12
Description:

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).*

(0)
Understand similarity in terms of similarity transformations.
Education Level: 9-12
Description:

Verify experimentally the properties of dilations given by a center and a scale factor:
-- a. 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.
-- b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

(0)
Apply trigonometry to general triangles.
Education Level: 9-12
Description:

Prove the Laws of Sines and Cosines and use them to solve problems.

(0)
Apply trigonometry to general triangles.
Education Level: 9-12
Description:

Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

(3)
Understand similarity in terms of similarity transformations.
Education Level: 9-12
Description:

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.

(0)
Understand similarity in terms of similarity transformations.
Education Level: 9-12
Description:

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