Course: CoYOTe Transformations and Similarity: Mastering Geometric Transformations

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.
Education Level: 10
Subject: math

The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Education Level: 10
Subject: math

Recognize transformations as functions that take points in the plane as inputs and give other points as outputs and describe the effect of dilations on two-dimensional figures.
Education Level: 10
Subject: math

Given two similar figures, describe a sequence of transformations that exhibits the similarity between them using coordinates and the non-coordinate plane.
Education Level: 10
Subject: math

Understand the meaning of similarity for two-dimensional figures as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
Education Level: 10
Subject: math

Construct arguments about triangles using theorems. 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, and AA.
Education Level: 12
Subject: math

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Education Level: 12
Subject: math

Show 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.
Education Level: 10
Subject: math

Explain and use the relationship between the sine and cosine of complementary angles.
Education Level: 10
Subject: math

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Education Level: 10
Subject: math

Derive the formula A = ½ ab sin C for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
Education Level: 12
Subject: math

Prove the Laws of Sines and Cosines and use them to solve problems.
Education Level: 12
Subject: math

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).
Education Level: 12
Subject: math