Postulates And Theorems Flashcards
(37 cards)
What is the Protractor Postulate?
For every angle A there corresponds a positive real number less than or equal to 180. This is symbolized 0 < m Pyramid A <_ 180
What is The Continuity Postualant?
If k is half-plane determined by AC then for every real number 0 < x < 180 there is exactly one ray AB that lies in k such that m BAC = x
What is the Ruler Postulate?
It’s every point of a line can be placed in correspondence with a real number.
What is the Completeness Postulate?
Given a ray AC and any positive real number r there is exactly one point c on the Ray so that AC= r
What is the Angle Addition Postulate?
If K lies in the interior of < MNP then m< MNK + m< KNP
What is theorem 4.1?
All right angles are congruent
What is theorem 4.2?
If two angles are adjacent and supplementary then they form a linear pair.
What is theorem 4.3?
Angles that from a linear pair are supplementary ?
What is theorem 4.4?
If one angle of a linear pair is a right angle, then the other angle is also a right angle.
What is theorem 4.5?
Vertical Angle Theorem
Vertical angles are congruent.
What is theorem 4.6?
Congruent supplementary are right angles.
What is theorem 3.2?
It’s the perimeter if a regular n-gon with sides of length s is n x s
What is the theorem 3.1 ?
Midpoint Theorem
If midpoint M is the midpoint of AB then AM = 1/2 AB
What is the Jordan Curve Theorem?
Any simple closed curve divides a plane into three disjoint sets: ether curve, it’s interior, it’s exterior.
What is the Plane Separation Postulate?
Every line divides any planes containing the line into three disjoint sets : the line and two half-planes.
What is the Line Separation Postulate?
Every point divides any line through that point into three disjoint sets : the point and two half-lines.
What is theorem 1.1 ?
If two distinct lines intersect , they intersect in one and only point.
What is theorem 1.2 ?
A lime and a point not on that line are contained in one and only one plane.
What is theorem 1.3 ?
Two intersecting lines are contained in one and only one plane.
What is theorem 1.4 ?
Two parallel lines are contained in one and only one plane.
What is theorem 5.1?
The conditional p -> q is equivalent to the disjunction ~q or p
What is theorem 5.2 ?
A conditional statement is equivalent to its contra positives. P -> q is equivalent to ~q -> ~p
What is theorem 6.1 ?
If two congruent segments are bisected, then the four resulting segments are congruent.
What is theorem 6.2 ?
Segment congruence is equivalent relation.
