Chapter 1 Flashcards
Conjecture
an unproven statement that is based on a pattern or observation
Inductive Reasoning
Looking for patterns and making conjectures is part of a process called inductive reasoning
Counterexample
an example that shows a conjecture is false
Undefined Terms
terms that cannot be mathematically defined using other words
Point
no dimension, represented by a dot
line
one dimension, extends without end and is represented by a line with two arrowheads
Plane
two dimensions, represented by a shape that looks like a floor or wall and extends without end
Postulates
statements that are accepted without further justification
Postulate 1 and 2
Through any two points there is exactly one line Through any three points not on a line there is exactly one plane
Collinear points
points that lie on the same line
Coplanar points
points that lie on the same plane
coplanar lines
lines that lie on the same plane
Segment
(A-B): consists of the endpoints A and B and all points on AB in between A and B
Ray
A–>B consists of the endpoint A and all points on AB that lie on the same side of A as B
they “intersect”
figures that have any points in common
intersection
two or more figures is the point or points that the figures have in common
Postulate 3 “Intersection of two lines”
If two lines intersect, then their intersection is a point
Postulate 4 “Intersection of two planes”
If two planes intersect, then their intersection is a line
Coordinate
the real number that corresponds to a point is the coordinate of the point
Distance
the absolute value of the difference of the coordinates of A and B AB is also called the length of A-B
Postulate 5 “Segment Addition” Postulate 6 “Angle addition postulate”
If B is between A and C then AC = AB + BC. If AC = AB + BC, then B is between A and C. If P is in the interior of angle RST, then the measure of angle RST is the sum of the measures of angle RSP and PST
Congruent segments
segments that have the same length Denoted by tick marks Symbol for indicating congruence is “≅” for now ill use =~
Angle
consists of two rays that have the same endpoint
Sides
The rays of the angle
Vertex
the endpoint of the angle name of an angle
Degrees
the measure of an Angle denoted by ° The measure of
Congruent angles
Two angles that have the same measure denoted by =~
Classifying angles by their measures
Acute angle, Obtuse angle, Right angle, Straight angle measure is between 0° and 90° measure is between 90° and 180° measure is 90° measure is 180°
