Section 1-1
Inductive Reasoning and Using Patterns
Inductive Reasoning- type of reasoning that allows you
to reach conclusions based on a pattern of specific examples or past events.
Conjecture- conclusion reached by using inductive reasoning
Patterns= pascals triangle, 2,4,6,8,10,12....
Section 1-2
Lines, Planes, Points
Point- represented by a small dot and is named by a Capital letter- a location that tells us where we are at
Space- set of all points
Line- series of points that extends in two opposite directions without end
Collinear- points that lie in the same line
Con collinear- not lined up, random points
Plane- a flat surface that extends in all directions without end
Coplanar- points and lines in the same plane
Postulate- 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, then they intersect in a line
Postulate 1-4: Through any three non collinear points there is exactly one plane
Section 1-3
Segments, Rays, Parallel lines and Planes
Segment- a part of a line consisting of one two endpoints and all points between them
Ray- part of a line consisting of one endpoint and all the points of the line on one side of the endpoint
Opposite ray- two collinear rays with the same endpoint opposite always form a
Line
Parallel lines- coplanar lines that do not intersect
Skew lines- don't lie on the same plane, they are neither parallel or intersecting
Parallel planes- planes that don't intersect
Postulate 1-7: protractor postulate
Postulate 1-8: angle addition postulate, If point B is in the interior of
Section 1-5
Polyglobs- three tenticles, three black dots, move in all different directions,
multi colored
Squiggles- zig zags or circular lines with a black dot on one end and a white dot on the other end
midpoint- point that divides a segment into two congruent segments
Segment Bisector- a line ray or segment that intersects the midpoint of a segment
Perpendicular lines- two lines that intersect to form right angles
Perpendicular Bisector- of a segment is a line, segment, or ray that is perpendicular to a segment at its midpoint, creates a
Right angle
Angle Bisector- ray that divides an angle into two congruent angles
Section 1-7
Using Inductive Reasoning
Deductive Reasoning- process of reasoning logically from the given facts to conclusion
Vertical Angles- two angles whose sides are opposite rays
Adjacent Angles- two coplanar angles with a common side, common vertex and no
common interior points
Complementary angles- two angles, the sum of whose measure is ninety degrees
Supplementary angles- two angles, the sum of whose measure is one hundred eighty degrees
Property of Congruence
Reflexive property= Line AB is congruent to line AB
Symmetric property=If line AB is congruent to line CD then line CD is congruent to line AB. IF Angle A is Congruent to Angle B, then Angle B is congruent to angle A.
Transitive property= If line AB is congruent to line CD and CD is congruent to line E,F then Line AB is congruent to line EF.
Theorems
Theorem- a conjecture that is proven
Proof- a convincing agreement that uses deductive reasoning
1-1 Vertical angles: vertical angles are congruent
1-2 Congruent supplements: If two angles are supplements of congruent angles or of the same angle, then the two angles are
Congruent
1-3 Congruent complements: If two angles are compliments of congruent's or the
same angle, then the two angles are congruent
Section 1-7 Angle pairs
Vertical angles- two angles whose sides are opposite rays
Adjacent angles- two coplanar angles with common vertex, common side, common ray, but no common interior points
Supplementary angles- two angles whose sum is always one hundred eighty degrees
Complementary angles- two angles whose sum is ninety degrees
Section 1-8
The Coordinate Plane
Distance formula=D=The square root of X1 - X2 squared plus y1 - y2 squared.
Midpoint formula= M= x1 plus x2 divided by 2, y1 plus y2 divided by 2.
Section's 2-1 thru 2-6
