Download Geom 1.3 - Postulates

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