Download Points, lines and planes Section 1-2 Point A basic unit of geometry

Chapter 1
REASONING IN
GEOMETRY
Section 1-1
PATTERNS AND
INDUCTIVE
REASONING
Inductive Reasoning
When you make a
conclusion based on a
pattern of examples or past
events
Conjecture
A conclusion that you reach
based on inductive
reasoning
Counterexample
An example that shows
your conjecture is false
It only takes one
counterexample to prove
your conjecture false
Examples
 Find the next three terms of
each sequence.
 11.2, 9.2, 7.2, …….
 1, 3, 7, 13, 21, …….

……..
Section 1-2
POINTS, LINES
AND PLANES
Point
A basic unit of geometry
Has no size
Named using capital letters
Line
 A series of points that extends
without end in two directions.
 Named with a single lowercase
letter or by two points on the
line
Collinear and Noncollinear
 Points that lie on the same line
 Points that do not lie on the
same line
Ray
 Has a definite starting point
and extends without end in
one direction
 Starting point is called the
endpoint
 Named using the endpoint
first, then another point
Line Segment
Has a definite beginning
and end
Part of a line
Named using endpoints
Plane
 A flat surface that extends
without end in all directions
 Named with a single
uppercase script letter or
three noncollinear points
Coplanar and Noncoplanar
 Points that lie in the same
plane
 Points that do not lie in the
same plane
Section 1-3
POSTULATES
Postulates
Facts about geometry that
are accepted as true
Postulate 1-1
Two points determine a
unique line
Postulate 1-2
If two distinct lines
intersect, then their
intersection is a point.
Postulate 1-3
Three noncollinear points
determine a unique plane.
Postulate 1-4
If two distinct planes
intersect, then their
intersection is a line.
Section 1-4
CONDITIONAL
STATEMENTS
AND THEIR
CONVERSES
Conditional Statement
 Written in if-then form
 Examples:
 If points are collinear, then
they lie on the same line.
 If a figure is a triangle, then it
has three angles.
 If two lines are parallel, then
they never intersect.
Hypothesis
 The part following the if
 If points are collinear, then
they lie on the same line.
 If a figure is a triangle, then it
has three angles.
 If two lines are parallel, then
they never intersect.
Conclusion
 The part following the then
 If points are collinear, then
they lie on the same line.
 If a figure is a triangle, then it
has three angles.
 If two lines are parallel, then
they never intersect.
Converse
 A conditional statement is
formed by exchanging the
hypothesis and the conclusion
in a conditional statement
Example
 Statement: If a figure is a triangle,
then it has three angles.
 Converse: If a figure has three
angles, then it is a triangle.
Section 1-6
A PLAN FOR
PROBLEM
SOLVING
Perimeter
The distance around a
figure
Formula
An equation that shows
how certain quantities are
related
Area
The number of square units
needed to cover the surface
of a figure