Euclidean Geometry: Understanding Undefined Terms and Postulates, Slides of Geometry

Download Euclidean Geometry: Understanding Undefined Terms and Postulates and more Slides Geometry in PDF only on Docsity! EUCLIDEAN GEOMETRY Undefined Terms & Postulates (Section 1-6, 1-7) VOCABULARY 1. _________________ 2. _________________ 3. _________________ Undefined Terms in Geometry: Dimensions: Undefined Terms in Geometry: VOCABULARY 1. _________________ 2. _________________ 3. _________________ Undefined Terms in Geometry: Point A (named with a single letter) Dimensions: Undefined Terms in Geometry: VOCABULARY 1. _________________ 2. _________________ 3. _________________ Undefined Terms in Geometry: Point Line A (named with a single letter) Dimensions: Undefined Terms in Geometry: VOCABULARY 1. _________________ 2. _________________ 3. _________________ Undefined Terms in Geometry: Point Line A (named with a single letter) A B Dimensions: Undefined Terms in Geometry: VOCABULARY 1. _________________ 2. _________________ 3. _________________ Undefined Terms in Geometry: Point Line Plane A (named with a single letter) A B (named with any two points on the line) C B A Dimensions: Undefined Terms in Geometry: VOCABULARY 1. _________________ 2. _________________ 3. _________________ Undefined Terms in Geometry: Point Line Plane A (named with a single letter) A B (named with any two points on the line) C B A (named with any three non- collinear points on the plane) Dimensions: Undefined Terms in Geometry: VOCABULARY 1. _________________ 2. _________________ 3. _________________ Undefined Terms in Geometry: Point Line Plane A (named with a single letter) A B (named with any two points on the line) C B A (named with any three non- collinear points on the plane) Dimensions: Undefined Terms in Geometry: One-Dimensional: an object where all points lie in a single line MORE VOCABULARY MORE VOCABULARY * Figure: a set of points MORE VOCABULARY Figure: a set of points Space: The set of all points MORE VOCABULARY Figure: a set of points Space: The set of all points Collinear: three or more points that lie on the same line Coplanar: four or more points that lie on the same plane Postulate: a statement that is assumed or generally accepted as true MORE VOCABULARY Figure: a set of points Space: The set of all points Collinear: three or more points that lie on the same line Coplanar: four or more points that lie on the same plane Postulate: a statement that is assumed or generally accepted as true Theorem: a statement that has been proven using postulates, properties, definitions or previously-proven theorems Point-Line-Plane Postulate Unique Line Assumption: Number Line Assumption: Point-Line-Plane Assumption: Through any two points, there is exactly one line. Every line is a set of points that can be put in a one-to- one correspondence with the real number line. Given a line on a plane, there is at least one point on the plane that is not on the line. INTERSECTIONS Line-Intersection Theorem: two different lines can intersect in at most one point INTERSECTIONS Line-Intersection Theorem: two different lines can intersect in at most one point INTERSECTIONS Line-Intersection Theorem: two different lines can intersect in at most one point Parallel Lines: lines that have no points in common, or lines that are identical