1 notes - Blackboard
... How many angles are shown in the diagram below? Name the different angles: X ...
... How many angles are shown in the diagram below? Name the different angles: X ...
Geometry standards Unit 2
... devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on t ...
... devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on t ...
VOCABULARY: Point, line, plane, collinear, coplanar, undefined
... geometry. Line segments, rays, angles, and polygons are introduced. Students explore congruent segments and angles, learn to construct them and expand knowledge of Pythagorean theorem to master the distance and midpoint formulas. ...
... geometry. Line segments, rays, angles, and polygons are introduced. Students explore congruent segments and angles, learn to construct them and expand knowledge of Pythagorean theorem to master the distance and midpoint formulas. ...
Performance Objective Articulation Worksheet Use this worksheet to
... Tangent- geometry: a line in the plane of a circle that intersects a circle at exactly one point trigonometry: in a right triangle, the ratio of the length of the leg opposite a given acute angle to the leg adjacent to the same angle Secant- a line that intersects a circle or some other curve at two ...
... Tangent- geometry: a line in the plane of a circle that intersects a circle at exactly one point trigonometry: in a right triangle, the ratio of the length of the leg opposite a given acute angle to the leg adjacent to the same angle Secant- a line that intersects a circle or some other curve at two ...
Section 2.1 – Undefined terms, postulates, segments and angles
... Postulate 2.1 – Every line contains at least two distinct points. Postulate 2.2 – Two points are contained in one and only one line. Postulate 2.3 – If two points are in a plane the line containing these points is also in the plane. Postulate 2.4 – Three non-collinear points are contained in one and ...
... Postulate 2.1 – Every line contains at least two distinct points. Postulate 2.2 – Two points are contained in one and only one line. Postulate 2.3 – If two points are in a plane the line containing these points is also in the plane. Postulate 2.4 – Three non-collinear points are contained in one and ...
Grade Level: Middle School/High School Class Title: Geometry
... a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. 2. Given two figures, use the definition of similarity ...
... a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. 2. Given two figures, use the definition of similarity ...
geometry journal 1
... Line: A straight connection of points that goes on forever in both directions. XY YX Segment: Any straight collection of dots that has a beginning and an end (endpoints) XY Ray: A straight collection of points that has one end point and goes on forever. XY *This are related because they all are ways ...
... Line: A straight connection of points that goes on forever in both directions. XY YX Segment: Any straight collection of dots that has a beginning and an end (endpoints) XY Ray: A straight collection of points that has one end point and goes on forever. XY *This are related because they all are ways ...
Power Standards for Geometry based on Common Core Standards
... 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 ...
... 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 ...
Geometry Additional Illustrated Vocabulary
... Rational Numbers: Any real number that can be expressed in the form a∕b where a and b are integers and b does not equal 0. Ray: A part of a line that has an endpoint and contains all the points of the lines without end in one direction. Real Numbers: The union of the sets of rational and irrational ...
... Rational Numbers: Any real number that can be expressed in the form a∕b where a and b are integers and b does not equal 0. Ray: A part of a line that has an endpoint and contains all the points of the lines without end in one direction. Real Numbers: The union of the sets of rational and irrational ...
Vocabulary Words Examples
... Rational Numbers: Any real number that can be expressed in the form a∕b where a and b are integers and b does not equal 0. Ray: A part of a line that has an endpoint and contains all the points of the lines without end in one direction. Real Numbers: The union of the sets of rational and irrational ...
... Rational Numbers: Any real number that can be expressed in the form a∕b where a and b are integers and b does not equal 0. Ray: A part of a line that has an endpoint and contains all the points of the lines without end in one direction. Real Numbers: The union of the sets of rational and irrational ...
09 Neutral Geometry I
... Euclid is the master. The Elements has been used as a standard geometry text up until this century—over 2000 years! After the bible it is the second most printed book of all time in western civilization (Mao’s Little Red Book is the second-most printed overall). We will vary a little from Euclid’s a ...
... Euclid is the master. The Elements has been used as a standard geometry text up until this century—over 2000 years! After the bible it is the second most printed book of all time in western civilization (Mao’s Little Red Book is the second-most printed overall). We will vary a little from Euclid’s a ...
Geometry Syllabus
... Angle Relationships in Circles Segment Relationships in Circles Circles in the Coordinate Plane ...
... Angle Relationships in Circles Segment Relationships in Circles Circles in the Coordinate Plane ...
Geometry Key Assignment 1 1 #1 - a) What is the intersection of
... d) Three ______________ points are required to determine a plane. e) _______ points define a line. ...
... d) Three ______________ points are required to determine a plane. e) _______ points define a line. ...
Chapter 6 Learning Objectives
... Learning Objectives for Chapter Six Circles Learning objectives indicate what you should be able to do upon completing your work in each of the textbook sections. Section 6.l: Circles and Related Segments and Angles 1. become familiar with the terminology (radius, center, chord, are, etc.) of the ci ...
... Learning Objectives for Chapter Six Circles Learning objectives indicate what you should be able to do upon completing your work in each of the textbook sections. Section 6.l: Circles and Related Segments and Angles 1. become familiar with the terminology (radius, center, chord, are, etc.) of the ci ...
Lie sphere geometry
Lie sphere geometry is a geometrical theory of planar or spatial geometry in which the fundamental concept is the circle or sphere. It was introduced by Sophus Lie in the nineteenth century. The main idea which leads to Lie sphere geometry is that lines (or planes) should be regarded as circles (or spheres) of infinite radius and that points in the plane (or space) should be regarded as circles (or spheres) of zero radius.The space of circles in the plane (or spheres in space), including points and lines (or planes) turns out to be a manifold known as the Lie quadric (a quadric hypersurface in projective space). Lie sphere geometry is the geometry of the Lie quadric and the Lie transformations which preserve it. This geometry can be difficult to visualize because Lie transformations do not preserve points in general: points can be transformed into circles (or spheres).To handle this, curves in the plane and surfaces in space are studied using their contact lifts, which are determined by their tangent spaces. This provides a natural realisation of the osculating circle to a curve, and the curvature spheres of a surface. It also allows for a natural treatment of Dupin cyclides and a conceptual solution of the problem of Apollonius.Lie sphere geometry can be defined in any dimension, but the case of the plane and 3-dimensional space are the most important. In the latter case, Lie noticed a remarkable similarity between the Lie quadric of spheres in 3-dimensions, and the space of lines in 3-dimensional projective space, which is also a quadric hypersurface in a 5-dimensional projective space, called the Plücker or Klein quadric. This similarity led Lie to his famous ""line-sphere correspondence"" between the space of lines and the space of spheres in 3-dimensional space.