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Geom 1.3 Postulates Postulates: Statements that we accept as true Start with Postulates, then build on them to create the rest of Geometry Our textbook: 26 postulates Euclid's Elements (c. 300 BCE): 5 postulates School of Athens, Rafael, 1509 Postulates (Axioms): • Be familiar with them • Don't memorize them by the textbook numbers • Make a diagram for each of the following postulates on Geogebra. You may: > Work with a partner > Print it out > Save it and send to me to print Geom 1.3 Postulates Textbook's first three axioms: 11: Two points determine a unique line. 12: If two distinct lines intersect, then their intersection is a point. 13: Three noncollinear points determine a unique plane. web.geogebra.org FYI: Euclid's 4+1 Postulates: 1. 2. 3. 4. 5. Two points determine a line segment. A line segment can be extended infinitely in both directions. A circle can be described by a center point and radius. All right angles are equal to each other. (Parallel Postulate) If a straight line intersects two other straight lines so that the interior angles on the same side are both less than right angles, the two straight lines, if extended indefinitely, will intersect on the same side as where the two angles are both less than right angles. Geom 1.3 Postulates Extra Points: Describe the history of the parallel postulate and nonEuclidean geometry. 11.5 pages of writing, plus nice diagrams. Email electronic version to me: Ethan@midpendragons.org