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Transcript 
Properties and Theorems
List of Theorems
Chapters 1-3
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Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
Law of Detachment
Law of Syllogism
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Reflexive Property
Transitive Property
Substitution Property
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Right Angle Congruence Theorem
Congruent Supplements Theorem
Congruent Complements Theorem
Linear Pair Postulate
Vertical Angles Theorem
Parallel Postulate
Perpendicular Postulate
Corresponding Angles Postulate &
Converse
Alternate Interior Angles Theorem &
Converse
Consecutive Interior Angles Theorem &
Converse
Alternate Exterior Angles Theorem &
Converse
List of Theorems
Chapter 4
Chapter 5
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Triangle Sum Theorem
Exterior Angle Theorem
Third Angles Theorem
SSS Congruence Postulate
SAS Congruence Postulate
ASA Congruence Postulate
AAS Congruence Postulate
Base Angles Theorem
Base Angles Converse
Hypotenuse-Leg Congruence
Theorem
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Perpendicular Bisector Theorem &
Converse
Angle Bisector Theorem & Converse
Concurrency of Perpendicular Bisectors
of a Triangle
Concurrency of Angle Bisectors of a
Triangle
Concurrency of Medians of a Triangle
Concurrency of Altitudes of a Triangle
Midsegment Theorem
Exterior Angle Inequality
Triangle Inequality
Hinge Theorem
Converse of Hinge Theorem
4.1 – Triangles and Angles
Types of Triangles
Types of Triangles
Right and Isosceles Triangles
Interior vs. Exterior Angles
Triangle Sum Theorem
Exterior Angle Theorem
Corollary to the Triangle Sum Theorem
Classify the triangle by its angles and
by its sides.
Classify the triangle by its angles and
by its sides.
Classify the triangle by its angles and
by its sides.
Complete the sentence with always,
sometimes, or never.
Sketch the following triangles, if
possible. If not possible, state so.
1. A right isosceles triangle
2. An obtuse scalene triangle
3. An acute equilateral triangle
4. A right obtuse triangle
Find the measure of the numbered
angles.
Find the measure of the numbered
angles.
Find the measure of the exterior
angle shown
x  80  ( y )  180
3x  22  y  180
x  80  3 x  22
80  2 x  22
102  2 x
51  x
x  51
Realize this last problem is an example
of the Exterior Angle Theorem
Find the measure of the exterior
angle shown
2 x  3  51  4 x  8
2 x  54  4 x  8
54  2 x  8
46  2 x
23  x
x  23
4(23)  8  92  8  100
mA  42
mB  2mA  8
mA  mB  mC  180
mB  2(42 )  8
mB  84  8
118  mC  180
mB  76
42  76  mC  180
mC  62
Exterior Angle C  180  mC
 180  62
 118
Homework
• pp 198-199 1-28 all, 31-39 all, 47,49-50
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