## 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 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.

# Standards: Math

(0)
Prove theorems involving similarity.
Education Level: 9-12
Description:

Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

(1)
Prove theorems involving similarity.
Education Level: 9-12
Description:

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

(2)
Define trigonometric ratios and solve problems involving right triangles.
Education Level: 9-12
Description:

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.

(0)
Define trigonometric ratios and solve problems involving right triangles.
Education Level: 9-12
Description:

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

(1)
Define trigonometric ratios and solve problems involving right triangles.
Education Level: 9-12
Description:

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

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

Derive the formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

(1)
Perform arithmetic operations with complex numbers.
Education Level: 9-12
Description:

Know there is a complex number i such that i^2 = −1, and every complex number has the form a + bi with a and b real.

(1)
Perform arithmetic operations with complex numbers.
Education Level: 9-12
Description:

Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

(1)
Perform arithmetic operations with complex numbers.
Education Level: 9-12
Description:

Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

(0)
Represent complex numbers and their operations on the complex plane.
Education Level: 9-12
Description:

Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

(0)
Represent complex numbers and their operations on the complex plane.
Education Level: 9-12
Description:

Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3i)^3 = 8 because (-1 + √3i) has modulus 2 and argument 120°.

(0)
Represent complex numbers and their operations on the complex plane.
Education Level: 9-12
Description:

Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

(0)
Use complex numbers in polynomial identities and equations.
Education Level: 9-12
Description:

Solve quadratic equations with real coefficients that have complex solutions.

(0)
Use complex numbers in polynomial identities and equations.
Education Level: 9-12
Description:

Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).

(0)
Use complex numbers in polynomial identities and equations.
Education Level: 9-12
Description:

Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.