- standard
Understand and apply theorems about circles
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Circles
Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; i…
- standard
Understand and apply theorems about circles
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Circles
Prove that all circles are similar.
- standard
Apply trigonometry to general triangles
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Similarity, Right Triangles, and Trigonometry
(+) 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.
- standard
Apply trigonometry to general triangles
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Similarity, Right Triangles, and Trigonometry
(+) 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, resu…
- standard
Apply trigonometry to general triangles
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Similarity, Right Triangles, and Trigonometry
(+) Prove the Laws of Sines and Cosines and use them to solve problems.
- standard
Define trigonometric ratios and solve problems involving right triangles
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Similarity, Right Triangles, and Trigonometry
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
- standard
Define trigonometric ratios and solve problems involving right triangles
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Similarity, Right Triangles, and Trigonometry
Explain and use the relationship between the sine and cosine of complementary angles.
- standard
Define trigonometric ratios and solve problems involving right triangles
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Similarity, Right Triangles, and Trigonometry
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for …
- standard
Prove theorems involving similarity
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Similarity, Right Triangles, and Trigonometry
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
- standard
Prove theorems involving similarity
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Similarity, Right Triangles, and Trigonometry
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagore…
- standard
Understand similarity in terms of similarity transformations
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Similarity, Right Triangles, and Trigonometry
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
- standard
Understand similarity in terms of similarity transformations
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Similarity, Right Triangles, and Trigonometry
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformati…
- standard
Understand similarity in terms of similarity transformations
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Similarity, Right Triangles, and Trigonometry
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
- standard
Understand similarity in terms of similarity transformations
- 9th - 12th Grade
- Michigan State Math Standards
- Geometry: Similarity, Right Triangles, and Trigonometry
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.