Definitions, Postulates, and Theorems

DEFINITIONS, POSTULATES, AND THEOREMS A definition uses known words to describe a new word. Point, Line, and Plane must be commonly understood without being defined. Undefined terms: Point- understood to be a dot that represents a location in a plane or in space. Line-understood to be straight, contains infinitely many points, extends infinitely in 2 directions, and has no thickness Plane-understood to be a flat surface that extends infinitely in all directions.

1) Definition – tells meaning of term. Definitions are always biconditional. 2) Postulate – rules that are accepted as being true 3) Theorems – rules which must be proven true. 4) Points Postulate- a line contains at least 2 points; a plane contains at least 3 non-collinear points; space contains at least 4 non-collinear, non-coplanar points. 5) Line Postulate- 2 points are contained in one and only one line. 6) Plane Postulate- 3 non-collinear points are contained in one and only one plane. 7) Flat Plane Postulate- If 2 points are contained in a plane, then the line through them is contained in the same plane. 8) Plane Intersection Postulate- If 2 planes intersect, then they intersect at a line. 9) Congruent- same size and shape 10) Similar- same shape does not have to be same size 11) Segment (def)- a straight path from one point to another. 12) Ray (def)- an endless straight path from a starting point. 13) Opposite Rays (def)- 2 rays that share a common endpoint to form a line. 14) Space (def)- the set of all points. 15) Collinear Points (def)- points that are contained in one line. 16) Non-collinear Points (def)- points NOT contained in the same line. 17) Coplanar Points (def)- points that are contained in the same plane. 18) Non-coplanar Points (def)- points NOT contained in the same plane. 19) Coplanar Lines (def)- lines that are contained in the same plane. 20) Non-coplanar Lines (def)- lines NOT contained in the same plane. 21) Angle (def)- is the union of two non-collinear rays which have the same endpoint. 22) Interior of an Angle (def)- inside of the angle 23) Exterior of an Angle (def)- outside of the angle. 24) Right Angle(def)- An is right its measure is 90º. 25) Acute Angle (def)- Acute angle < 90 26) Obtuse Angle (def)- Obtuse angle > 90 27) Straight Angles (def)- Straight angle = 180. 28) Segment Addition Postulate – If point P is between points A and B, then AP + PB = AB. Sum of parts equal whole. 29) Angle Addition Postulate- If B is in the interior of

Properties from Algebra: Let a, b, and c be real numbers. Addition Property If a = b, then a + c = b + c. (add same thing to both sides of an equation) Subtraction Property If a = b, then a – c = b – c. (subtract same thing from both sides of an equation) Multiplication Property If a = b, then ac = bc. (multiply both sides by same thing) Division Property If a = b and c = 0, then a / c = b / c. (divide both sides by the same thing) Reflexive Property For and real number a, a = a. Symmetric Property If a = b, then b = a. Transitive Property If a = b and b = c, then a = c. Substitution Property If a = b, then a may be substituted for b in any equation or expression. Distributive property If a(b + c), then ab + ac.

Formulas to Know: Distance Midpoint

x+ x y + y d=( x - x )2 + ( y - y ) 2 (1 2 , 1 2 ) 2 1 2 1 2 2