Postulates and Theorems
Theorems
Postulates
Theorems
- Midpoint Theorem: If a point is the midpoint of a segment, then it divides the segment into two smaller segments that are equal to one half of the length of the original segment.
- Vertical Angles Theorem: If two angles are vertical angles, then they are congruent.
- Linear Pair Theorem: If two angles form a linear pair, then they are supplementary.
- Right Angle Congruence Theorem: All right angles are congruent.
- Congruent Complements Theorem: If two angles are complementary to the same angle (or to two congruent angles), then the two angles are congruent.
- Congruent Supplements Theorem: If two angles are supplementary to the same angle (or to two congruent angles), then the two angles are congruent.
- Common Segments Theorem: Given collinear points A, B, C, and D arranged on a segment such that A and D are the endpoints, B is between A and C, and C is between B and D. If AB = CD, then AC = BD.
Postulates
- Through any two points there is exactly one line.
- Through any three noncollinear points there is exactly one plane.
- If two points lie in a plane, then the line containing those points lies in the plane.
- If two unique lines intersect, then they intersect at exactly one point.
- If two unique planes intersect, then they intersect at exactly one line.
- Segment Addition Postulate: If B is between A and C, then AB + BC = AC.
- Ruler Postulate: The points on a line can be put into a one-to-one correspondence with the real numbers.
- Protractor Postulate: Given AB and a point O on AB, all rays that can be drawn from O can be put into a one-to-one correspondence with the real numbers from 0 to 180.
- Angle Addition Postulate: If S is in the interior of ∠PQR, then m∠PQS + m∠SQR = m∠PQR.
|
|
|