Chapter 1 Flashcards
Conjecture
A conclusion you reach during inductive reasoning
Inductive Reasoning
Is reasoning that is based on patterns you observe. If you observe a pattern in a sequence you can use inductive reasoning to tell what the next term in the sequence will be
Counter example
To a conjecture is an example for which the conjecture is incorrect - proving it false
Point
Has no size. It is represented by a small dot and is named by a capital letter
Space
Defined as the set of all points
A line
Is a series of points that extends in two opposite directions without end
Collinear points
Are points that lie on the same line
A plan
Is a flat surface that has no thickness. it contains many lines and extends without end in the directions of all it’s lines. Name it with a single capital letter or at least 3 of its non collinear points.
Postulate or Axiom
Is an accepted statement of fact
Postulate 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 the intersect at exactly one line
Postulate 1-4
Through any three non collinear points there is exactly one plane
A segment
The part of a line consisting of two end points and all points between them
A ray
Is the part of a line consisting of one endpoint and all points of the line on one side of the endpoint
Opposite Rays
Two collinear rays with the same endpoint. Also they always form a line
Parallel lines
Lines that do not intersect
Skew line
Non-Coplanar not parallel and do not intersect
Parallel plane
Planes that do no intersect a line and a plane that do not intersect are also parallel
Postulate 1-5 ruler postulate
The points of a line can be put into one to one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference of the corresponding number
Postulate 1-6 Segment Addition
If three points A,B, and C are collinear and B is between A and C ten AB + Bc = AC
Coordinate
Distance from the origin
Congruent
Two segments with the same length
Midpoint of segment
A point that divides the segment into two congruent segments. A midpoint or any line, ray of other segment through a midpoint, is said to have bisect the segment
Postulate 1-7 protractor postulate
Let OA(Ray) and OB(Ray) be opposite rays in a plane. OA and OB an all the rays with a endpoint of O that can be drawn on one side of AB( Line) can be paired with the real numbers from 0-180 so that OA is paired with 0 and Ob is paired with 180 . If OC is with x and OD with Y then m<COD = |x-y|
Postulate 1-8 Angle addition
If point B is in the interior of <BOC = 180
Angle
Is formed by two rays with the same endpoint
Acute Angle
Less than 180 degree angle
Obtuse angle
Greater than 90 degrees but less than 180 degrees
Straight Angle
180 degree always
Congruent angle
Are angles with the same measure
Vertical angles
Are two angles who’s sides are opposite rays
Adjacent angles
Are two Coplanar angles with a common side, common vertex, and no common internal points
Complimentary Angles
Are two angles who’s measure have a sum of 90 degrees
Supplementary angles
Are two angles who’s measures have a sum of 180 degrees
Distance formula
The distance between two point can be found by this
Midpoint formula
Coordinates of the midpoint m of segment AB with end points
