+

# Mathematics Geometry

## Common Core Standards

### Mathematics: Geometry

In Geometry, instructional time should focus on developing students’ understanding of Euclidean geometry in three major areas: (1) developing the concepts of congruence, similarity, and symmetry through the use of geometric transformations; (2) defining sine, cosine, and tangent for right triangles and extending the use of these functions to the Pythagorean Theorem as well as the Law of Sine and Law of Cosine; (3) developing students’ understanding of analytical and dynamic geometry, allowing the use of algebra in geometry problems and vice versa.
Sophia and Common Core Standards
Our Many Ways to Learn method makes it easy to integrate the new standards into your teaching. By using multiple instructors and teaching styles for each tutorial, we make sure you're reaching your students, so they can reach their goals.
Note: Our Common Core-aligned content is middle and high school-focused. We're continually expanding our library, so stay tuned - more great content coming soon.

## G.CO - Congruence

##### Understand congruence in terms of rigid motions
Code
Standard
Concepts
G.CO.6
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 the definition of congruence in terms of rigid motions to decide if they are congruent.
3
##### Prove geometric theorems
Code
Standard
Concepts
G.CO.9
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
1

## G.SRT - Similarity, Right Triangles, and Trigonometry

##### Understand similarity in terms of similarity transformations
Code
Standard
Concepts
G.SRT.2
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.
2
##### Define trigonometric ratios and solve problems involving right triangles
Code
Standard
Concepts
G.SRT.8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★
6

## G.MG - Modeling with Geometry

##### Apply geometric concepts in modeling situations
Code
Standard
Concepts
G.MG.2
Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).★
1