Postulate 1: Line VS contains Points V and S.
Postulate 2: Planes V and S are intersected by Line BW.
Postulate 3: Through Points V and S, Line VS exists.
Postulate 4: Plane C contains Points V,S, and B.
Postulate 5: Points V and S lie in Plane M, and the line containing them also lies in Plane M.
Postulate 6: Through Points V,B, and S, only Plane C exists.
Postulate 7: Lines v and s intersect at Point B.
|
Page by: Vinny Shirvaikar, 8th grader at Vandeventer Middle School
Geometry is built on theorems and postulates, so naturally, we learn a lot of them in class. Here are most of the ones we have been taught so far. Postulates with Visual Representations: 1. A line contains at least two points. This is one of the most basic postulates in geometry. I chose it because it is vital to all future understanding of planes and, basically, any further geometry construction. 2. If two planes intersect, then their intersection is a line. This is another really important postulate in the world of geometry. Just like number 1, we have to understand this before moving to more complex things. 3. Through any two points, there exists exactly one line. My reason for choosing this postulate is the exact same as the first two. In order to learn and comprehend further geometry studies, this is one postulate that must be known. 4. A plane contains at least three noncollinear points. Some people can get confused about whether two points can make a plane, or if it is certain that four noncollinear points will make a plane. I included this specific postulate to clear up that confusion. 5. If two points lie in a plane, then the line containing them lies in that plane. Again- this is a fundamental postulate when it comes to more complex ones. 6. Through any three noncollinear points, there exists exactly one plane. This postulate is basically the same as number four. 7. If two lines intersect, then their intersection is exactly one point. If one doesn't learn this postulate before moving on in geometry, he will be helpless when he tries to learn bigger things. Postulates without Visual Representations: 8. Ruler Postulate- The points on a line can be put in a one-on-one correspondence with the real numbers 9. Segment Addition Postulate- If Point B is between Points A and C, then AB+BC = AC. 10. Linear Pair Postulate- If two angles make a linear pair, then they are supplementary. Theorems: 1. Right Angle Congruence Theorem- All right angles are congruent. 2. Congruent Supplements Theorem- If two angles are congruent, then their supplements are congruent. 3. Vertical Angles Theorem- Vertical angles are congruent. |