Geometry
... Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of t ...
... Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of t ...
4.1 Congruent Figures
... • Two figures are congruent if and only if their vertices can be matched up so that corresponding parts (angles and sides) of the figures are congruent. • When writing which figures are congruent, be sure to write the vertices in the same order. ...
... • Two figures are congruent if and only if their vertices can be matched up so that corresponding parts (angles and sides) of the figures are congruent. • When writing which figures are congruent, be sure to write the vertices in the same order. ...
O`Neill`s Math
... common geometric figures. 16.0 Perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. 22.0 Know the effects of rigid motion on figures in the coordinate plane and space, includ ...
... common geometric figures. 16.0 Perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. 22.0 Know the effects of rigid motion on figures in the coordinate plane and space, includ ...
Non-Euclidean Geometry Unit
... plane geometry, the basic concepts are points and lines. In spherical geometry, points are defined in the usual way, but lines are defined such that the shortest distance between two points lies along them. Therefore, lines in spherical geometry are Great Circles. A Great Circle is the largest circl ...
... plane geometry, the basic concepts are points and lines. In spherical geometry, points are defined in the usual way, but lines are defined such that the shortest distance between two points lies along them. Therefore, lines in spherical geometry are Great Circles. A Great Circle is the largest circl ...
GETE0303
... 29. If two lines in a plane do not meet, then the lines are parallel. If two lines in a plane are parallel, they do not meet. Two lines in a plane do not meet if and only if the lines are parallel. Chapter 3 Parallel and Perpendicular Lines ...
... 29. If two lines in a plane do not meet, then the lines are parallel. If two lines in a plane are parallel, they do not meet. Two lines in a plane do not meet if and only if the lines are parallel. Chapter 3 Parallel and Perpendicular Lines ...
1/1 - Math K-12
... There is exactly one line through any two points. There is exactly one plane through any three noncollinear points. ...
... There is exactly one line through any two points. There is exactly one plane through any three noncollinear points. ...
The parallel postulate, the other four and Relativity
... P1. To draw a straight line from any point A to any other B. P2. To produce a finite straight line AB continuously in a straight line. P3. To describe a circle with any centre and distance. P1, P2 are unique. P4. That, all right angles are equal to each other. P5. That, if a straight line falling on ...
... P1. To draw a straight line from any point A to any other B. P2. To produce a finite straight line AB continuously in a straight line. P3. To describe a circle with any centre and distance. P1, P2 are unique. P4. That, all right angles are equal to each other. P5. That, if a straight line falling on ...
Geometry Kindergarten Identify and describe shapes. CCSS.MATH
... Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of t ...
... Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of t ...
Glossary
... vertex that is not in the same plane as the base. The lateral surface consists of all segments that connect the vertex with points on the edge of the base. The altitude, or height, is the perpendicular distance between the vertex and the plane that contains the base. ...
... vertex that is not in the same plane as the base. The lateral surface consists of all segments that connect the vertex with points on the edge of the base. The altitude, or height, is the perpendicular distance between the vertex and the plane that contains the base. ...
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.