Mathematics | Course : Model Mathematics II (Integrated Pathway)
Domain - Similarity, Right Triangles, and Trigonometry
Cluster - Prove theorems involving similarity using a variety of ways of writing proofs, showing validity of underlying reasoning.
[MII.G-SRT.B.5] - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
- Congruent
Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations). - Proof
A proof of a mathematical statement is a detailed explanation of how that statement follows logically from statements already accepted as true.
[MI.G-CO.B.8] -
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
[MI.G-GPE.B.5] -
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).
[MII.G-SRT.A.3] -
Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar.
[PC.F-TF.C.9] -
(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
[AQR.F-TF.C.9] -
(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.