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### 27 Cards in this Set

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 MIDPOINT a point M is the midpoint of line segment STif and only if M is between S and T and SM = MT postulate 2-4 COMPLETENESS PROPERTY FOR POINTS IN THE PLANE (FOR GRAPH) FOR EACH POINT IN A COORDINATE PLANE CORRESPONDS TO ONLY ONE ORDERED PAIR (X,Y) OF REAL NUMBERS. AND EACH ORDERED PAIR OF REAL NUMBERS CORRESPONDS TO ONE POINT ON THE COORDINATE PLANE. postulate 2-1 THE NUMBER LINE POSTULATE each real number corresponds to one and only one point on the number line. Each point on the number line corresponds to 1 real number! SYMMETRIC PROPERTY of equality for real numbers for any numbers a and b if a=b then b=a 9each side looks like a mirror image of the other side) REAL numbers includes RATIONAL and IRRATIONAL numbers postulate 2-2 DISTANCE POSTULATE for any two points on a number line and a given unit of measure, there is a unique positive real number called the MEASURE of distance between the 2 points THEOREM 2-6 MIDPOINT FORMULA FOR A COORDINATE PLANE x one + x two ----------------- 2 and y one + y two ______________-__ 2 REFLEXIVE PROPERTY of equality for real numbers for any number a then: a=a MULTIPLICATION AND DIVISION PROPERTIES of equality for real numbers for any numbers: a, b, and c if a x c = b x c mult and if c is not equal to zero if a/c = b/c division(can't have 0 in denomin congruence of line segments is symmetric SEE PAGE 63 TRANSATIVE PROPERTY of equality for real numbers for any numbers (can be more than 3) a, b, and c if a=b and b=c then a=c CONGRUENT SEGMENTS two segments are congruent if and only if they have the same length Congruence of line segments is REFLEXIVE see pg 63 VECTOR a DIRECTED line segment if shows movement is a certain direction. Magnitude=length of vector. arrowhead=direction of vector ADDITION AND SUBTRACTION of equality for real numbers for any numbers a, b, and c if a=b then; a+c=b+c and addition a-c=b-c subtraction postulate 2-3 RULER POSTULATE the points on a line can be pared with the real numbers so that the measure of the distance between corresponding points is the positive (absolute value) distance of the 2 numbers PRECISION OF MEASUREMENT depends on the smallest unit of measure being used eg 1/16 in. GREATEST POSSIBE ERROR IS ONE-HALF THE SMALLEST UNIT OF MEASURE (EG 1/2OF 1/16 OR 1/32 INCH) congruence of line segments is TRANSATIVE see page 63 MEASUREMENTS measurements such as 10 inches are composed of 2 parts 10 (the number of units) inches(the unit of measure) check to include the U of M RATIONAL numbers any number written as a/b wher a and b are intergers (whole numbers) and b is not zero ************* definition of BETWEENNESS 3 COLINNEAR POINTS IF R IS BETWEEN POINT P AND POINT Q THEN: PR + RQ = PQ theorm 2-5 MIDPOINT FORMULA FOR A NUMBER LINE A+B _________ 2 IRRATIONAL numbers decimals that to not end and do not repeat example 0.66666666 etc or pi 3.141 etc THEORM 2-4 IF a and b are real numbers, a vertical line contains all points (x,y)such that x=a and a horizontal line contains all points (x,y) suth that y=b the equation of a vertical line is x=a and the equation of a horizontal line is y=b COORDINATE of a line the NUMBER that corresponds to the point (address) on the line WHOLE numbers includes zero and the counting numbers SUBSTITUTION PROPERTY of equality for ral numbers for any numbers a and b if a=b then a may be replaced by b in any equation (you can substitute one for the other)