Plane Geometry: Postulates in Geometry

Plane Geometry
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Postulates in Geometry:

(1) Through two given points one and only one straight line can be drawn.
(2) A straight line is the shortest line that can be drawn two points.
(3) A straight line may be extended indefinitely or it may be limited at any point.
(4) A circle or part of one may be drawn about any point as the center and with any given radius.
(5) A geometric figure may be freely moved in space without any change in form or size.
(6 - Parallel Postulate) Through a given point one and only one straight line can be drawn parallel to a given line.
(6.1 - Parallel Postulate Corollary) If two straight lines are parallel to a third straight line, they are parallel to each other.

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Plane Geometry: Principles in Geometry

Plane Geometry Principles in Geometry (1) A straight line is the shortest line between two points. (2) Only one straight line can be drawn between two points. (3) Two straight lines intersect at only one point. (4) Quantities (Lines) equal to the same quantity (line) are equal to each other. (5) The whole is equal to the sum of all its parts. (6) The whole is greater than any of its parts. (7) If equals are added to equals, then the sums are equal. (8) If equals are subtracted from equals then the remainders are equal. (9) Doubles of equals are equal. (10) Halves of equals are equal. (11) If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third. (12) All straight lines are equal.

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