G-SRT. Similarity, Right Triangles, and Trigonometry

G-SRT.A. Understand similarity in terms of similarity transformations

G-SRT.A.1. Verify experimentally the properties of dilations given by a center and a scale factor:

• Dilating a Line

G-SRT.A.1.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.

• Dilating a Line

G-SRT.A.1.b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

• Dilating a Line

G-SRT.A.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.

• Are They Similar?
• Congruent and Similar Triangles
• Similar Quadrilaterals
• Similar Triangles

G-SRT.A.3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

• Similar triangles

G-SRT.B. Prove theorems involving similarity

G-SRT.B.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.

• Joining two midpoints of sides of a triangle
• Pythagorean Theorem

G-SRT.B.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

• Bank Shot
• Congruence of parallelograms
• Extensions, Bisections and Dissections in a Rectangle
• Finding triangle coordinates
• Folding a square into thirds
• How far is the horizon?
• Is this a rectangle?
• Points from Directions
• Slope Criterion for Perpendicular Lines
• Tangent Line to Two Circles
• Unit Squares and Triangles

G-SRT.C. Define trigonometric ratios and solve problems involving right triangles

• Finding the Area of an Equilateral Triangle
• Mt. Whitney to Death Valley
• Seven Circles I

G-SRT.C.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.

• Defining Trigonometric Ratios
• Tangent of Acute Angles

G-SRT.C.7. Explain and use the relationship between the sine and cosine of complementary angles.

• Sine and Cosine of Complementary Angles
• Trigonometric Function Values

G-SRT.C.8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

• Ask the Pilot
• Coins in a circular pattern
• Constructing Special Angles
• Neglecting the Curvature of the Earth
• Setting Up Sprinklers
• Seven Circles III
• Shortest line segment from a point $P$ to a line $L$

G-SRT.D. Apply trigonometry to general triangles

• Seven Circles III

G-SRT.D.9. 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.

• No tasks yet illustrate this standard.

G-SRT.D.10. Prove the Laws of Sines and Cosines and use them to solve problems.

• No tasks yet illustrate this standard.

G-SRT.D.11. 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, resultant forces).

• No tasks yet illustrate this standard.