Chapter 3 Flashcards
(34 cards)
a = a (Any number id equal to itself)
Reflexive Property
If a = b, then a can be substituted for b in any expression.
Substitution Property
If a = b, then a+c = b+c
Addition Property
If a =b, then a-c = b-c
Subtraction Property
If a = b, then ac = bc
Multiplication Property
If a = b and c ≠ 0, then a/c = b/c
Division Property
The Ruler Postulate
The points on a line can be numbered so that positive number differences measure distances.
Definition (Betweenness of Points)
A point is between two other points iff its coordinates are between their coordinates.
The Betweenness of Points Theorem
If A-B-C, then AB + BC = AC
Acute
Iff it is less than 90 degrees.
Right
Iff it is equal to 90 degrees.
Obtuse
Iff more it is ore than 90 degrees.
Straight
Iff it is 180 degrees.
The Protractor Postulate
The rays in a half-rotation can be numbered form 0-180 degrees so that the positive number differences measure angles.
Definition (Betweenness of Rays)
A ray is between two others in the same half-rotation iff its coordinate in between their coordinate.
The Betweenness of Rays Theorem
If OA-OB-OC, then
Definition of a Midpoint
A point is the midpoint iff it divides the line segment into two equal parts.
Definition of a Bisection
A line bisects an angle iff it divides the angle into two equal angles.
Congruent
Coinciding exactly when superimposed.
Corollary
A corollary in a theorem that can be easily proved as a consequence of a postulate or a theorem.
Corollary to the Ruler Postulate
A line segment has exactly one midpoint.
Corollary to the Protractor Postulate
An angle has exactly one ray that bisects it.
Definition of Complementary
Two angles are complementary iff their sum is 90 degrees.
Definition of Supplementary
Two angles are supplementary iff their sum is 180 degrees.
