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Tools of Geometry

Inductive Reasoning *reasoning that is based on patterns you observe.3, 6, 12, 24,... Using inductive reasoning, you can infer that each number is multiplyed by two. So, the next two terms will be 48 and 96.
Conjecture A conclusion you reach using inductive reasoning.* 1 = 1 = 1^2 * 1+3 = 4 = 2^2 * 1+3+5 = 9 = 3^2 * 1+3+5+7= 16= 4^2 * Using inductive reasoning, you can conclude that the perfect squares form a pattern.
Counterexample If a conjecture is false, then find an example to prove it.
Point A location represented as a small dot, named by a capital letter.
Space Space is defined as the set of all points
Line A series of points that extends in two opposite directions without end.
Collinear points Points that lie on the same line
Plane A flat surface that has no thickness and extends in all directions without end.
Coplanar Points and lines in the same plane.
Postulate/Axiom An accepted state or fact.
Postualte 1.1 Through any two points there is exactly one line.
Postulate 1.2 If two lines intersect, then they intersect in exactly one point.
Postulate 1.3 If two planes intersect, then they intersect in exactly one line
Postulate 1.4 Through any three noncollinear points there is exactly one plane.
Segment The part of a line consisting of two endpoints and all points between them.
Ray The part of a line consisting of one endpoint and all the points on one side of the endpoint.
Opposite Rays Two collinear rays with the same endpoint; opposite rays always form a line.
Parallel Lines Coplanar lines that do not intersect.
Skew Lines Skew lines are noncoplanar; therefore, they are not parallel and do not intersect.
Parallel Planes Planes that do not intersect, and are not skew.
Ruler Postulate (Postulate 1.5) The distance on a line, segment, or ray is the absolute value of the difference of the two corresponding numbers. * Ex: Segment A=6 and C=14*6-14=-8 * Abs.val. of -8 = 8 * The distance of segment AC = 8
Congruent Segments Two segments with the same length are congruent (≡) segments. * Ex: If AB = CD, then Line AB ≡ Line CD
Segment Addition Potulate (Postulate 1.6) If three points A,B,C are collinear and B is between A and C, then AB + BC = AC.
Midpoint A point that divides a segment in two congruent segments.
Angle Two rays with the same endpoint (vertex).
Protractor Postulate (Postulate 1.7) Any angle can only measure one degree at a time. * Ex: an angle at 30degrees can't be at 40degrees.
Acute Angle 0 < X < 90
Right Angle X = 90
Obtuse Angle 90 < X < 180
Straight Angle X = 180
Angle Addition Postulate (Postualte 1.8) If point B is in the interior of ∠AOC, then m∠AOB + m∠BOC = m∠AOC. * If ∠AOC is a straight angle, then m∠AOB + m∠BOC = 180.
Congruent Angles Angles with the same measure. * Ex: If m(angle)1 = m(angle)2, then (angle)1 ≡ (angle)2
Perpendicular Lines Two lines that intersect to form right angles. (looks like an "X")
Perpendicular Bisector A line, segment, or ray that is perpendicular to the segment at its midpoint, thereby bisecting the segment into two congruent segments.
Angle Bisector A ray that divides an angle into two congruent coplanar angles. Its endpoint is at the engle vertex.
The Distance Formula The distance "d" between two points A(x<sub>1, y<sub>1) and B(x<sub>2,y<sub>2)is ** d= ((square root))(x<sub>2-x<sub>1)^2 + (y<sub>2-y<sub>1)^2.
The Midpoint Formula The coordinates of the midpoint M of Line AB with endpoints A(x<sub>1,y<sub>1) and B(x<sub>2,y<sub>2) are the following:*M= ((x<sub>1+x<sub>2)[all over]2, (y<sub>1+y<sub>2)[all over] 2)
Created by: Abzter323