Geometry – Chapters 1 and 2
1-2 Points, Lines, and Planes
Point
Definition
Line
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Symbol
Line Segment
Endpoint
Ray
Plane
Opposite Rays
Space
Collinear Points
Coplanar
Postulate or
Axiom
Postulate 1-1
Through any two points there is exactly
one line.
Intersection
Postulate 1-2
If two distinct lines intersect,
then they intersect in exactly one point.
Postulate 1-3
If two distinct planes intersect,
then they intersect in exactly one line.
Postulate 1-4
Through any three noncollinear points
there is exactly one plane.
1-3 Measuring Segments
Postulate 1-5
Every point on a line can be paired with a real numbers.
Ruler Postulate
Distance between
points
Measuring
Segment Lengths
Postulate 1-6
Segment Addition
Postulate
If three points A, B, and C are collinear
and B is
between A and C, then AB + BC = AC.
Segment Bisector
Midpoint
1-7 Midpoint and Distance in the Coordinate Plane
How to find the
midpoint given 2
endpoints…
How to find the
other endpoint
when given 1
endpoint and the
midpoint…
Distance Formula
How to find the
distance of a
segment…
Pythagorean
Theorem
1-4 Measuring Angles
Definition
Symbol
Angle
Sides
Vertex
Interior region
Exterior region
Postulate 1-7
Protractor
Postulate
How to measure
an angle…
Every ray on an angle can be paired one to one with a real number from 0 to 180
on a protractor.
Types of Angles
Definition
# of
Degrees
Acute
Right
Obtuse
Straight
Reflexive
Congruent Angles
Symbols for
Congruent Angles
Postulate 1-8
Angle Addition
Postulate
If point B is in the interior of <AOC, then
m<AOB + m<BOC = m<AOC
1-5 Exploring Angle Pairs
Special Angle
Pairs
Adjacent Angles
Vertical Angles
Supplementary
Angles
Complementary
Angles
Special Markings
on Lines and
Angles
Linear Pair
Definitions
Angle #s
Draw an example
Postulate 1-9
Linear Pair
Postulate
Angle Bisector
How to find angle
measures using
an angle
bisector…
If two angles form a linear pair, then
they are supplementary.
Geometry - Chapter 2
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2-5 Reasoning in Algebra and Geometry
Algebraic Properties of Equality
Addition Property
Subtraction
Property
Multiplication
Property
Division Property
Reflexive Property
Symmetric Property
Transitive Property
Substitution
Property
Distributive Property
Additive Inverse
Property
Multiplicative
Inverse Property
Additive Identity
Property
Multiplicative
Identity Property
Multiplicative
Property of Zero
Properties of Congruence
Reflexive Property
Symmetric Property
Transitive Property
Proof
Two-Column
Proof –
Lists each
statement on the
left and the
justification, or
the reason for
each statement,
on the right.
A convincing argument
2-6 Proving Angles Congruent
Conjecture
An “educated” guess, or a guess that you give thought to
Theorem
A conjecture or statement that you can prove true.
Theorem 2-1
Vertical Angles
Theorem
Vertical angles are congruent.
List the vertical angles:
If … Then
Statements
Hypothesis
The “if” part or conditional
Conclusion
The “then” part or the conclusion
Paragraph Proof
The statements and
justifications are
written in sentences
in a paragraph
instead of in two
columns.
Theorem 2-2
Congruent
Supplements
Theorem
If two angles are supplements of the same
angle (or of congruent angles), then the two
angles are congruent.
Theorem 2-3
Congruent
Complements
Theorem
If two angles are complements of the same
angle (or of congruent angles), then the two
angles are congruent.
Theorem 2-4
All right angles are congruent.
Theorem 2-5
If two angles are congruent and
supplementary, then each is a right angle.