Izzy Kurkulis September 28, 2013 EXTRA CREDIT GEOMETRY
... Two Perpendicular theorem: If two coplanar lines l and m are each perpendicular to the same lines, then they are parallel to each other. Perpendicular to parallels theorem: In a plane if a line is perpendicular to to one of two parallel lines, then it is also perpendicular to the other. Perpen ...
... Two Perpendicular theorem: If two coplanar lines l and m are each perpendicular to the same lines, then they are parallel to each other. Perpendicular to parallels theorem: In a plane if a line is perpendicular to to one of two parallel lines, then it is also perpendicular to the other. Perpen ...
The discovery of non-Euclidean geometries
... The first use of Postulate 5 occurs only in Proposition 29 (If a transversal cuts two parallel lines, the alternate interior angles are equal, the corresponding angles are equal, and the interior angles on one side of the transversal sum to two right angles) Everything before that depends only o ...
... The first use of Postulate 5 occurs only in Proposition 29 (If a transversal cuts two parallel lines, the alternate interior angles are equal, the corresponding angles are equal, and the interior angles on one side of the transversal sum to two right angles) Everything before that depends only o ...
MGS43 Geometry 3 Fall Curriculum Map
... Investigate, justify, and apply theorems about the sum of the measures of the interior and exterior angles of polygons Investigate, justify, and apply theorems about each interior and exterior angle measure of regular polygons Investigate, justify, and apply theorems about parallelograms involving ...
... Investigate, justify, and apply theorems about the sum of the measures of the interior and exterior angles of polygons Investigate, justify, and apply theorems about each interior and exterior angle measure of regular polygons Investigate, justify, and apply theorems about parallelograms involving ...
Revised Geometry Pacing Calendar
... What strategies can we use to determine the sum of the interior angles of any polygon? What is the sum of the exterior angles of any polygon? What is the relationship between the midsegments and the sides of a triangle? (Extension to trapezoids) What are the properties of a parallelogram? How can we ...
... What strategies can we use to determine the sum of the interior angles of any polygon? What is the sum of the exterior angles of any polygon? What is the relationship between the midsegments and the sides of a triangle? (Extension to trapezoids) What are the properties of a parallelogram? How can we ...
The Word Geometry
... In any triangle, each exterior angle equals the sum of the two remote interior angles. If two parallel lines are cut by a transversal, the alternate interior angles are equal, and the corresponding angles are equal. ...
... In any triangle, each exterior angle equals the sum of the two remote interior angles. If two parallel lines are cut by a transversal, the alternate interior angles are equal, and the corresponding angles are equal. ...
Andrew Ryba Math Intel Research Final Paper 6/7/09 (revision 6/17
... In the diagram, three lines IA, IB, and ID are shown as ordinary blue lines. A dotted blue ray (marked p) that makes an angle of 90 with ID is also shown. The angle between this ray and the ray IB is 270 – θ – φ. A second dotted blue ray (marked q) bisects this angle. Copies of the bisected angle ar ...
... In the diagram, three lines IA, IB, and ID are shown as ordinary blue lines. A dotted blue ray (marked p) that makes an angle of 90 with ID is also shown. The angle between this ray and the ray IB is 270 – θ – φ. A second dotted blue ray (marked q) bisects this angle. Copies of the bisected angle ar ...
Analytic geometry
In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.Analytic geometry is widely used in physics and engineering, and is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry.Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes in three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space (three dimensions). As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. The numerical output, however, might also be a vector or a shape. That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom.