SIMILARITY, RIGHT TRIANGLES, AND TRIGONOMETRY (G.SRT)

UNDERSTANDING SIMILARITY IN TERMS OF SIMILARITY TRANSFORMATIONS

MCC9‐12.G.SRT.1 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.   
MCC9‐12.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.  
MCC9‐12.G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. 

mcc9-12.g.srt.1

Khan Academy
1. Dilations or scaling around a point

MCC9-12.G.SRT.2

Khan Academy
1. Similarity and Transformations

MCC9-12.G.SRT.3

Khan Academy
1. Triangle Similarity

PROVING THEOREMS INVOLVING SIMILARITY

MCC9‐12.G.SRT.4 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.   
MCC9‐12.G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.  

MCC9-12.G.SRT.4

Khan Academy
1. Triangle Similarity
2. Pythagorean Theorem

MCC9-12.G.SRT.5

DEFINE TRIGONOMETRIC RATIOS AND SOLVE PROBLEMS INVOLVING RIGHT TRIANLGES

MCC9-12.G.SRT.6 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. 
MCC9-12.G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. 
MCC9-12.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. 

MCC9-12.G.SRT.6

Khan Academy
1. Special Right Triangles
2. Trig ratios and similarity

MCC9-12.G.SRT.7

Khan Academy
1. Sine, cosine and tangent trigonometric functions 

MCC9-12.G.SRT.8

Khan Academy
1. Pythagorean Theorem