Support Material (SA-1)
... obvious notions, axioms / postulates and theorems. The five postulates of Euclid. Equivalent versions of the fifth postulate. Showing the relationship between axiom and theorem, for example : (Axiom) 1. Given two distinct points, there exists one and only one line through them. (Theorem) 2. (Prove) ...
... obvious notions, axioms / postulates and theorems. The five postulates of Euclid. Equivalent versions of the fifth postulate. Showing the relationship between axiom and theorem, for example : (Axiom) 1. Given two distinct points, there exists one and only one line through them. (Theorem) 2. (Prove) ...
Lesson 13
... manipulatives that modeled rigid motions (e.g., transparencies) because you could actually see that a figure was not altered, as far as length or angle was concerned. It is important to hold onto this idea while studying all of the rigid motions. Constructing rotations precisely can be challenging. ...
... manipulatives that modeled rigid motions (e.g., transparencies) because you could actually see that a figure was not altered, as far as length or angle was concerned. It is important to hold onto this idea while studying all of the rigid motions. Constructing rotations precisely can be challenging. ...
Geometry Honors - Belvidere School District
... Review solving systems of equations, slope, and writing the equation of a line from Algebra 1. Use slope to determine whether two lines are parallel, perpendicular, or intersecting. Solve problems by writing linear equations. Unit Rationale: Many buildings are designed using basic shapes, lines, and ...
... Review solving systems of equations, slope, and writing the equation of a line from Algebra 1. Use slope to determine whether two lines are parallel, perpendicular, or intersecting. Solve problems by writing linear equations. Unit Rationale: Many buildings are designed using basic shapes, lines, and ...
parallel lines
... Example 3 You are building a CD rack. You cut the sides, bottom, and top so that each corner is composed of two 45o angles. Prove that the top and bottom front edges of the CD rack are parallel. ...
... Example 3 You are building a CD rack. You cut the sides, bottom, and top so that each corner is composed of two 45o angles. Prove that the top and bottom front edges of the CD rack are parallel. ...
parallel lines
... Example 6 Line l1 has equation y = -2x +1. Find an equation for the line, l2 that passes through point (4, 0) and is perpendicular to l1. What is the slope of l1? ______________ What form is l1 written in? _______________________________ What does the slope of l2 need to be if they are perpendicular ...
... Example 6 Line l1 has equation y = -2x +1. Find an equation for the line, l2 that passes through point (4, 0) and is perpendicular to l1. What is the slope of l1? ______________ What form is l1 written in? _______________________________ What does the slope of l2 need to be if they are perpendicular ...
HS Standards Course Transition Document 2012
... Course Course name name a. Experiment with transformations in the plane. (CCSS: G-CO) i. State precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. (CCSS: G ...
... Course Course name name a. Experiment with transformations in the plane. (CCSS: G-CO) i. State precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. (CCSS: G ...
Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, n Cartesian coordinates (an element of real n-space) specify the point in an n-dimensional Euclidean space for any dimension n. These coordinates are equal, up to sign, to distances from the point to n mutually perpendicular hyperplanes.The invention of Cartesian coordinates in the 17th century by René Descartes (Latinized name: Cartesius) revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. Using the Cartesian coordinate system, geometric shapes (such as curves) can be described by Cartesian equations: algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2 in a plane may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4.Cartesian coordinates are the foundation of analytic geometry, and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra, complex analysis, differential geometry, multivariate calculus, group theory and more. A familiar example is the concept of the graph of a function. Cartesian coordinates are also essential tools for most applied disciplines that deal with geometry, including astronomy, physics, engineering and many more. They are the most common coordinate system used in computer graphics, computer-aided geometric design and other geometry-related data processing.