Secondary Mathematics II

Strand: GEOMETRY - Expressing Geometric Properties With Equations (G.GPE)

Translate between the geometric description and the equation for a conic section (Standard G.GPE.1). Use coordinates to prove simple geometric theorems algebraically. Include simple proofs involving circles (Standard G.GPE.4). Use coordinates to prove simple geometric theorems algebraically (Standard G.GPE.6).
• Coordinates of equilateral triangles
The purpose of this Illustrative Mathematics task is to examine angles of triangles whose vertices have specific integer coordinates.
• Coordinates of Points on a Circle
The purpose of this task it to use geometry and algebra in order to understand the behavior of the trigonometric function f(x)=sinx+cosx. The task has been stated in an open ended fashion as there are natural solutions using geometry, or using the trigonometric identity sin2x=2sinxcosx, or algebraically solving a system of equations.
• Explaining the equation for a circle
Starting with explicit cases, this task derives the formula for an arbitrary circle in the plane.
• Finding Equations of Parallel and Perpendicular Lines
This lesson unit is intended to help educators assess how well students are able to understand the relationship between the slopes of parallel and perpendicular lines.
• Finding triangle coordinates
The purpose of this task is to use similar triangles in order to study the coordinates of points which divide a line segment in a given ratio.
• GEOMETRY - Expressing Geometric Properties With Equations (G.GPE) - Sec Math II Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics II - Expressing Geometric Properties with Equations (G.GPE).
• Module 6: Similarity & Right Triangle Trigonometry - Student Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 6, Similarity and Right Triangle Trigonometry, introduces the last of the transformations, dilation. A big idea of Module 6 is that two figures are similar if a sequence of rigid transformation and dilations exists that maps one figure onto the other.
• Module 6: Similarity & Right Triangle Trigonometry - Teacher Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 6, Similarity and Right Triangle Trigonometry, introduces the last of the transformations, dilation. A big idea of Module 6 is that two figures are similar if a sequence of rigid transformation and dilations exists that maps one figure onto the other.
• Module 8: Circles & Other Conics - Student Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 8, Circles and Other Conics, takes an algebraic approach to solving problems with circles, parabolas, and in the Honors course, ellipses and hyperbolas. The module includes several hands- on explorations to develop the equations for circles, parabolas, and ellipses.
• Module 8: Circles & Other Conics - Teacher Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 8, Circles and Other Conics, takes an algebraic approach to solving problems with circles, parabolas, and in the Honors course, ellipses and hyperbolas. The module includes several hands- on explorations to develop the equations for circles, parabolas, and ellipses.
• Scaling a Triangle in the Coordinate Plane
The goal of this task is to apply dilations to a triangle in the coordinate plane.
• Slope Criterion for Perpendicular Lines
The goal of this task is to use similar triangles to establish the slope criterion for perpendicular lines.
• Slopes and Circles
The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever AXB is a right angle.
• Sorting Equations of Circles 2
This lesson unit is intended to help educators assess how well students are able to translate between the equations of circles and their geometric features, and sketch a circle from its equation.