Standard: 8.EE.6

Subject Area: Mathematics (NYS P-12 Common Core)

Grades: Intermediate, 8th Grade

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Standard: G-CO.10

Subject Area: Mathematics (NYS P-12 Common Core)

Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade

Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Standard: G-SRT.2

Subject Area: Mathematics (NYS P-12 Common Core)

Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade

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.

Standard: G-SRT.3

Subject Area: Mathematics (NYS P-12 Common Core)

Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade

Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Standard: G-SRT.4

Subject Area: Mathematics (NYS P-12 Common Core)

Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade

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.