HS Geometry - Catalina Foothills School District
... 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. HS.G-SRT.2 Given two figures use the definition of simi ...
... 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. HS.G-SRT.2 Given two figures use the definition of simi ...
file - Athens Academy
... Bisectors of a pair of interior angles on the same side of a transversal Two congruent adjacent angles Slopes of perpendicular lines Two lines crossed by a transversal A pair of exterior angles on the same side of a transversal Two planes parallel to the same line Two lines perpendicul ...
... Bisectors of a pair of interior angles on the same side of a transversal Two congruent adjacent angles Slopes of perpendicular lines Two lines crossed by a transversal A pair of exterior angles on the same side of a transversal Two planes parallel to the same line Two lines perpendicul ...
Geometry
... 1. Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, and ...
... 1. Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, and ...
Unit 3 Similarity and Congruence in Transformations Unit Overview
... G-CO-8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. G-SRT-2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity t ...
... G-CO-8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. G-SRT-2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity t ...
Critical - Archdiocese of Chicago
... Use Geometer’s Sketchpad, if available to construct the perpendicular bisector. Prove that every point that lies on the perpendicular bisector is equidistant from the endpoints of the ...
... Use Geometer’s Sketchpad, if available to construct the perpendicular bisector. Prove that every point that lies on the perpendicular bisector is equidistant from the endpoints of the ...
Geometric Transformations Sequence
... parabola when translations are applied? Students notice themselves or are guided to the realization that these are just the shifts and dilations of the graphs they know analytically. Students visualize that, for example, a graph of a quadratic function y = (x – p)2 + q corresponds to the translat ...
... parabola when translations are applied? Students notice themselves or are guided to the realization that these are just the shifts and dilations of the graphs they know analytically. Students visualize that, for example, a graph of a quadratic function y = (x – p)2 + q corresponds to the translat ...
Geometry Fundamentals - Art of Problem Solving
... from each of its vertices. Two players play the following game: Each player, in turn, signs his or her name on a previously unsigned face. The winner is the player who first succeeds in signing three faces that share a common vertex. Show that the player who signs first will always win by playing as ...
... from each of its vertices. Two players play the following game: Each player, in turn, signs his or her name on a previously unsigned face. The winner is the player who first succeeds in signing three faces that share a common vertex. Show that the player who signs first will always win by playing as ...
ABSE 025 Rev May 2014 - Glendale Community College
... Catalog Statement Adult Basic and Secondary Education 025 is the first half of a one -year high school level geometry course. In this course the notion of two-dimensional shapes as part of the Euclidian Plane and exploration of transformations of this plane as a way to determine whether two shapes a ...
... Catalog Statement Adult Basic and Secondary Education 025 is the first half of a one -year high school level geometry course. In this course the notion of two-dimensional shapes as part of the Euclidian Plane and exploration of transformations of this plane as a way to determine whether two shapes a ...
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.