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Name:____________________
Geometry Theorems Chapters 1-4 KEEP THIS IN YOUR NOTES FOR
EVER!!!!! IT IS SUPER USEFUL
Postulate 1: If there are two points, then there
is_____________________________ that contains them.
Postulate 3: If there are three points, then there
is_____________________________ that contains
them.
The Ruler Postulate:
Points on a line can be numbered so
that:_____________________________________________
Distance between points can be calculated
by:__________________________________________
Betweeness of Points Theorem: If B is between points A and C
then we can write the equation:
=_____+______
Linear Pairs Theorem: If two angles are a linear pair then they
are ____________________________
Vertical Angles Theorem: If two angles are vertical angles then
they are________________________
Pythagorean
Theorem:__________________________________________________________________
Substitution Property of Equality: If two things are equal, then
they can be____________________ for
each other.
Transitive Property of
Equality:______________________________________________________
Addition Property of
Equality:_______________________________________________________
Subtraction Property of
Equality:_____________________________________________________
Multiplication Property of
Equality:___________________________________________________
Division Property of
Equality:________________________________________________________
Square Root Property of
Equality:____________________________________________________
Reflexive Property of
Equality:_______________________________________________________
Theorem 2.2: If two angles are congruent and supplementary, then
each is a _______________________
Theorem 2.3: If two angles are both supplementary to a third
angle, then theyre___________________
to each other.
Theorem 2.4: If two angles are both complementary to a third
angle, then theyre ___________________
to each other
Alternate Interior Angles Theorem: Two lines are _______________
if and only if their alternate
interior angles are_____________________.
Alternate Exterior Angles Theorem: Two lines are _______________
if and only if their alternate
exterior angles are_____________________.
Corresponding Angles Theorem: Two lines are _______________ if
and only if their corresponding
angles are_____________________.
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Same Side Interior Angles Theorem: Two lines are _______________
if and only if their same side
interior angles are_____________________.
Same Side Exterior Angles Theorem: Two lines are _______________
if and only if their same side
exterior angles are_____________________.
Transitivity of Parallel Lines Theorem: If and then
________________
Theorem 3.8: If and then _________________________
Triangle Sum Theorem: The sum of the three interior angles of a
triangle is always________________
Exterior Angle Theorem: An exterior angle equals the
______________ of the remote interior angles.
Corresponding Parts of Congruent Triangles are Congruent Theorem
(CPCTC Thm): If two
triangles are congruent, then all their corresponding parts
are___________________________
Third Angle Theorem: If two triangles have two angles that are
congruent, then their third angles are also
__________________
Reflexive Property of Congruence: Any figure is always
__________________ to itself.
Transitive Property of Congruence: If shape A is congruent to
shape B and shape B is congruent to shape
C
then________________________________________________________________________
SSS Postulate: If two triangles have all three corresponding
sides congruent, then the triangles themselves
are________________________________
ASA Postulate: If two triangles have a corresponding
____________, _____________ and __________
congruent, then the triangles are congruent.
AAS Postulate: If two triangles have a corresponding
____________, _____________ and __________
congruent, then the triangles are congruent.
SAS Postulate: If two triangles have a corresponding
____________, _____________ and __________
congruent, then the triangles are congruent.
Some Useful Vocabulary that is also used in proofs
Bisect: Something is cut into two _________________ pieces
Midpoint: The point that divides a line segment into two
____________________ pieces
Right Angle: An angle that measures_________ degrees. NOTE: ALL
RIGHT ANGLES ARE
CONGRUENT TO EACH OTHER!!!
Perpendicular Bisector: A line segment that cuts another line
into two congruent pieces and does it at a 90
degree angle.
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Name:_____________________ Date:__________________
Classwork
(1) Look through your list of theorems and decide which theorem
justifies each conclusion below.
Given: + 3 = 7 Conclusion = 4
Reason:________________
Given: 1 = 25 Conclusion: 2 = 25
Reason:_______________
Given Line and line
Conclusion:
Reason:__________________
Given:
Conclusion: The triangles are
congruent.
Reason:_________________
Given:
Conclusion: = 110
Reason:__________________
Given: 1 is supplementary to 2 and 2 is supplementary to
3 Conclusion: 1 = 3
Reason:__________________
Given: Line and line
Conclusion:
Reason:__________________
Given: Point is between points and Conclusion: + =
Reason:__________________
Given: Ray bisects Conclusion: =
Reason:__________________
Given: is complementary to and is complementary to Conclusion:
=
Reason:__________________
Given: 1 = 45 Conclusion: 2 = 135
Reason:______________
Given: the diagram
Conclusion: The
triangles are
congruent
Reason:________
Given:
1 = 2 Conclusion:
Reason:_________________
Given: The triangles are
congruent
Conclusion:
3 = 2
Reason:_______
Given: the diagram
Conclusion:
= 60
Reason:__________________
Given: A is the midpoint of CR
Conclusion: =
Reason:_________________
Given: Conclusion:
1 = 2
Reason:_________________
Given: The diagram
Conclusion:
=
Reason:________________
4-3 Recognizing Theorems and using them in Proofs
1
2
1
2
70 40
75
45
1 2
1 2
2
3
C A R
67
33
67
33
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(2) Come up with your own conclusions AND the reasons.
Given Line and line
Conclusion:______________
Reason:__________________
Given: Conclusion:
__________
__________
Reason:_________________
Given:
1 = 2 Conclusion:
__________
Reason:_________________
Given: diagram
Conclusion
__________
__________________
Reason:___________
Given:
Conclusion:______________
Reason:__________________
Given: Line and line
Conclusion:
Reason:__________________
Given: the diagram
Conclusion: ______________
Reason:__________________
Given: 1 = 32 Conclusion:_________
Reason:_______________
Given: E is the midpoint of BT
Conclusion:______________
Reason:_________________
Given: Ray bisects Conclusion:_______________
________________________
Reason:__________________
Given: 1 = 36 Conclusion:__________
Reason:______________
Given:
Conclusion: _____________
_______________________
Reason:_________________
Given: The diagram
Conclusion:
____________
Reason:________________
Given: The triangles are
congruent
Conclusion: ______________
Reason:_________
Given: 2 = 49
Conclusion_______________
Reason:________________
Given: 1 is supplementary to 2 and 2 is supplementary to
3
Conclusion:_______________
Reason:__________________
Given: Point is between points and
Conclusion:_______________
Reason:__________________
Given: 1 is complementary to 2 and 2 is complementary to
3
Conclusion:_______________
Reason:__________________
1 2
82 34
68
52
1
2
1
2
1
2
B E T
60
80
60
80
B
C
A
D
