Download Chapter 4: Postulates of Lines, Line Segments

Chapter 4: Postulates of Lines, Line Segments, & Angles
Postulates:
1)
2)
A line segment can be extended to any length in either
direction.
Through any two points, one & only one line can be drawn.
(Two points determine a line.)
3)
Two lines cannot intersect in more than one point.
4)
One & only one circle can be drawn with any given point as a
center and the length of any given line segment as a radius.
5)
At a given point on a given line, one & only one
perpendicular can be drawn to the line.
6)
From a given point not on a given line, one & only one
perpendicular can be drawn to the line.
7)
For any two distinct points, there is only one positive real
number that is called the length of the line segment joining
the two points.
The shortest path between two points is the line segment
joining these two points.
8)
9)
A line segment has one & only one midpoint.
10)
An angle has one & only one bisector.
Reflexive
Property
Symmetric
Property
Transitive
Property
Equivalent Relation of Congruence:
Any geometric figure is congruent to itself.
Congruence may be expressed in either order.
Two geometric figures congruent to the same geometric
figure are congruent to each other.
Definitions:
Midpoint
Bisector
Congruent
Parts
Adjacent
Angles
Complementary
Angles
Supplementary
Angles
Linear Pair
Vertical Angles
Congruent
Polygons
CPCTC
The point the divides the segment into two congruent
segments.
A line or subset of a line that divides the segment or angle
into two congruent segments or angles.
Parts that have the same (equal) measures.
Two angles in the same plane that have a common vertex
and a common side but no interior points in common.
Two angles the sum of whose measures is 90.
Two angles the sum of whose measures is 180.
Two adjacent angles whose sum is a straight angle (180
degrees).
Two angles in which the sides of one angle are opposite
rays to the sides of the second angle.
Two polygons are congruent if and only if there is a 1 to 1
correspondence between their vertices such that
corresponding angles & corresponding sides are congruent.
~OR ~
CPCPC: Corresponding parts of congruent polygons
are congruent.
Also: Corresponding parts of congruent polygons are
equal in measure.
Corresponding parts of congruent triangles are congruent.
Theorems:
If two angles are right angles, then they are congruent.
If two angles are straight angles, then they are congruent.
If two angles are compliments of the same angle, they are congruent.
If two angles are congruent then their compliments are congruent.
If two angles are supplements of the same angle, they are congruent.
If two angles are congruent then their supplements are congruent.
If two angles form a linear pair, then they are supplementary.
If two lines intersect to form congruent adjacent angles, then they are
perpendicular.
If two lines intersect then the vertical angles are congruent.