Angles and Polar Coordinates
... lines, and compare it to a full circle • We divide the circle into 360 equal parts • See how many of those parts will fit in between the two lines ...
... lines, and compare it to a full circle • We divide the circle into 360 equal parts • See how many of those parts will fit in between the two lines ...
File
... The Ruler Postulate: Points on a line can be paired with the real numbers in such a way that: • Any two chosen points can be paired with 0 and 1. • The distance between any two points on a number line is the absolute value of the difference of the real numbers corresponding to the points. ...
... The Ruler Postulate: Points on a line can be paired with the real numbers in such a way that: • Any two chosen points can be paired with 0 and 1. • The distance between any two points on a number line is the absolute value of the difference of the real numbers corresponding to the points. ...
Common Core Geometry
... double reflections over intersecting lines (rotation), glide reflections and others. We will also discuss how the order of the composite transformations often changes the result. In addition we look at transformations working backwards. Given a pre-image and an image determine the composite transfor ...
... double reflections over intersecting lines (rotation), glide reflections and others. We will also discuss how the order of the composite transformations often changes the result. In addition we look at transformations working backwards. Given a pre-image and an image determine the composite transfor ...
CMP2: Kaleidoscopes, Hubcaps, and Mirrors (8th) Goals
... Identify angles (acute, right, obtuse, and straight). Identify and label the vertex, rays, and interior and exterior of an angle. Use appropriate naming conventions to identify angles. Identify the legs and hypotenuse of a right triangle. Use proportional reasoning to solve problems related to simil ...
... Identify angles (acute, right, obtuse, and straight). Identify and label the vertex, rays, and interior and exterior of an angle. Use appropriate naming conventions to identify angles. Identify the legs and hypotenuse of a right triangle. Use proportional reasoning to solve problems related to simil ...
week5
... Congruent segments are segments that have the same length. The symbol is . *Remember: When talking about sets, we know that equivalent sets have the same number of elements and equal sets have the same elements in each set. Equivalent segments are called congruent Segments consisting of identi ...
... Congruent segments are segments that have the same length. The symbol is . *Remember: When talking about sets, we know that equivalent sets have the same number of elements and equal sets have the same elements in each set. Equivalent segments are called congruent Segments consisting of identi ...
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.