Theorem, Postulate and Corollary List

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Theorem, Postulate and Corollary List

1

CHAPTER 2 REASONING AND PROOF


Postulates 2.1


2.7







Theorem 2.1


Midpoint Theorem


Postulate 2.8


Ruler Postulate




Postulate 2.9


Segment Addition Postulate



Theorem 2.2
Segment Congruence











2

Postulate 2.10 Protractor Postulate






Postulate 2.11 Angle Addition Postulate




Theorems
2.3

and 2.4

Supplement and Complement Theorems






Theorem 2.5











3

Theorems 2.6 and 2.7








Theorem 2.8 Vertical Angle
Theorem



T
heorems 2.9


2.13


Right Angle Theorems





CHAPTER 3 PARALLEL AND PERPENDICULAR LINES

Postulate 3.1 Corresponding Angles Postulate










4

Theorem 3.1



3.3 Parallel Lines and Angle Pairs








Theorem 3.4 Perpendicular Transversal Theorem



Postulate 3.2

and 3.3 Parallel and Perpendicular Lines



Postulate 3.4













5

Postulate 3.5 Parallel Postulate



Theorems 3.5


3.
8

Proving Lines Parallel










Theorem 3.9



CHAPTER 4 CONGRUENT TRIANGLES

Theorem 4.1 Angle Sum

Theorem










6

Theorem 4.2 Third Angle Theorem





Theorem 4.3 Exterior Angle Theorem




Cor
ollaries

4.1 and 4.2






Theorem 4.4 Properties of Triangle Congruence












7

Postulate 4.1 Side
-
Side
-
Side Congruence (SSS)





Postulate 4.2 Side
-
Angle
-
Side Congruence
(SAS)





Postulate 4.3 Angle
-
Side
-
Angle Congruence (ASA)


T
heorem 4.5 Angle
-
Angle
-
Side Congruence (AAS)











8

Theorem 4.6
-
4.8 and Postulate 4.4 Right Triangle Congruence










Theorem 4.9

Isosceles Triangle Theorem






Theorem 4.10













9

Corollaries 4.3 and 4.4





CHAPTER 5 RELATIONSHIPS IN TRIANGLES

Theorem 5.1

and 5.2 Points on Perpendicular Bisectors






Theorem 5.3




Theorems 5.4 and 5.5

Points on Angle Bisectors











10


Theorem 5.6 Incenter Theorem




Theorem 5.7 Centroid

Theorem




Theorem 5.8 Exterior Angle Inequality Theorem





Theorem 5.9



Theorem 5.10










11

T
heorem 5.11 Triangle Inequality Theorem



Theorem 5.12




Corollary 5.1




Theorem 5.13 SAS Inequality/Hinge Theorem





Theorem 5.14 SSS Inequality











12

CHAPTER 6 QUADRILATERALS

Theorem 6.1 Interior Angle Sum Theorem




Theorem 6.2 Exterior Angle Sum Theorem





Theorem
s

6.3

-

6.6

















13

Theorem 6.7




Theorem 6.8




Theorem
s

6.9



6.12 Proving Parallelograms



















14

Theorem 6.13



Theorem 6.14





Theorem
s

6.15



6.17 Rhombus








Theorem 6.18

and 6.19 Isosceles Trapezoid











15

Theorem 6.20




CHAPTER 7 Proportions and similarity

Postulate 7.1 Angle
-
Angle (AA) Similarity




Theorem 7.1

and 7.2








Theorem 7.3










16

Theorem 7.4

Triangle Proportionality Theorem









Theorem 7.5

Converse of the Triangle Proportionality Theorem




Theorem 7.6

Triangle Midsegment Theorem





Corollaries 7.1 and 7.2













17

Theorem 7.7

Proportional Perimeters Theorem


Theorem 7.8



7.10 Special Segments of Similar Triangles















Theorem 7.11 Angle Bisector Theorem










18

CHAPTER 8 RIGHT TRIANGLES AND TRIGONOMETRY

Theorem 8.1




Theorem 8.2




Theorem 8.3




Theorem 8.4 Pythagorean Theorem




Theorem 8.5 Converse

of the Pythagorean Theorem










19

Theorem 8.6




Theorem 8.7





Theorem 8.8

Law of Sines





Theorem 8.9 Law of Cosines













20

CHAPTER 9 TRANSFORMATIONS

Theorem 9.1

and Corollary 9.1





Theorem 9.2




Theorem 9.3



CHAPTER 10 CIRCLES

Theorem
10.1



Postulate 10.1 Arc Addition Postulate










21

Theorem 10.2






Theorem 10.3





Theorem 10.4



Theorem 10.5 Inscribed Angle Theorem













22

Theorem 10.6





Theorem 10.7



Theorem 10.8




Theorem 10.9



Theorem 10.10



Theorem 10.11









23

Theorem 10.12





Theorem 10.13






Theorem 10.14
















24

Theorem 10.15




Theorem 10.16





Theorem 10.17






CHAPTER 11 AREA OF POLYGONS AND CIRCLES

Postulate 11.1


Postulate 11
.2









25

CHAPTER 13 VOLUME

Theorem 13.1