Learning Area
... Consists of two rays of the same length B Consists of two rays of the same length that intersect at a vertex C Consists of two rays of different lengths that intersect at a vertex D Consists of two rays of different lengths that do not intersect at a vertex A transversal is a A Line that cuts parall ...
... Consists of two rays of the same length B Consists of two rays of the same length that intersect at a vertex C Consists of two rays of different lengths that intersect at a vertex D Consists of two rays of different lengths that do not intersect at a vertex A transversal is a A Line that cuts parall ...
Unit 1: Similarity, Congruence and Proofs
... 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. MCC9-12.G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using s ...
... 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. MCC9-12.G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using s ...
definitions and theorems 6 - The Bronx High School of Science
... A circle is a set of points in a plane such that the points are equidistant froma fixed point called the center of the circle. A radius of a circle is a line segment from the center of the circle to any point of the circle. A central angle of a circle is n angle whose vertex is the center of t ...
... A circle is a set of points in a plane such that the points are equidistant froma fixed point called the center of the circle. A radius of a circle is a line segment from the center of the circle to any point of the circle. A central angle of a circle is n angle whose vertex is the center of t ...
Glossary of Terms - Geneseo Migrant Center
... elements (of a set): the objects that belong to a set. ellipse: a plane curve whose path is that of a point, and the sum of whose distances from two fixed points (called the foci) is a constant. ...
... elements (of a set): the objects that belong to a set. ellipse: a plane curve whose path is that of a point, and the sum of whose distances from two fixed points (called the foci) is a constant. ...
Congruence and Constructions 23 Days Unit 2
... ● Use the undefined notion of a point, line, distance along a line and distance around a circular arc to develop definitions for angles, circles, parallel lines, perpendicular lines and line segments. ○ use point, line, distance along a line and/or distance around a circular arc to give a precise de ...
... ● Use the undefined notion of a point, line, distance along a line and distance around a circular arc to develop definitions for angles, circles, parallel lines, perpendicular lines and line segments. ○ use point, line, distance along a line and/or distance around a circular arc to give a precise de ...
- wced curriculum development
... Dividing a line into equal parts Given the line to be divided Draw a light construction line at any convenient angle from one end of the given line. With dividers or scale, set off from the intersections of the lines as many equal divisions as needed (in this example, three). Connect the last divisi ...
... Dividing a line into equal parts Given the line to be divided Draw a light construction line at any convenient angle from one end of the given line. With dividers or scale, set off from the intersections of the lines as many equal divisions as needed (in this example, three). Connect the last divisi ...
Mathematics Chapter: Tangents to Circles - JSUNIL tutorial
... Again, the length of common internal tangent to these two circles is 7 units. We can draw it as – ...
... Again, the length of common internal tangent to these two circles is 7 units. We can draw it as – ...
definitions and theorems 6 part 1 - The Bronx High School of Science
... A minor arc is an arc less than a semicircle, referred to with two letters: AB The measure of an arc ( m AB ) is equal to the measure of the central angle intercepting it. Congruent arcs are arcs of the same or congruent circles that are equal in measure. An inscribed angle of a circle is an ...
... A minor arc is an arc less than a semicircle, referred to with two letters: AB The measure of an arc ( m AB ) is equal to the measure of the central angle intercepting it. Congruent arcs are arcs of the same or congruent circles that are equal in measure. An inscribed angle of a circle is an ...
Lesson 1: Thales` Theorem
... Every lesson in this module is about an overlay of two intersecting lines and a circle. This will be pointed out to students later in the module, but keep this in mind while presenting the lessons. In this lesson, students investigate what some say is the oldest recorded result, with proof, in the h ...
... Every lesson in this module is about an overlay of two intersecting lines and a circle. This will be pointed out to students later in the module, but keep this in mind while presenting the lessons. In this lesson, students investigate what some say is the oldest recorded result, with proof, in the h ...
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.