Theorem, Postulate and Corollary List

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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

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Postulate 2.10 Protractor Postulate

Postulate 2.11 Angle Addition Postulate

Theorems 2.3 and 2.4 Supplement and Complement Theorems

Theorem 2.5

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Theorems 2.6 and 2.7

Theorem 2.8 Vertical Angle Theorem

Theorems 2.9 – 2.13 Right Angle Theorems

CHAPTER 3 PARALLEL AND PERPENDICULAR LINES

Postulate 3.1 Corresponding Angles Postulate

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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

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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

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Theorem 4.2 Third Angle Theorem

Theorem 4.3 Exterior Angle Theorem

Corollaries 4.1 and 4.2

Theorem 4.4 Properties of Triangle Congruence

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Postulate 4.1 Side-Side-Side Congruence (SSS)

Postulate 4.2 Side-Angle-Side Congruence (SAS)

Postulate 4.3 Angle-Side-Angle Congruence (ASA)

Theorem 4.5 Angle-Angle-Side Congruence (AAS)

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Theorem 4.6-4.8 and Postulate 4.4 Right Triangle Congruence

Theorem 4.9 Isosceles Triangle Theorem

Theorem 4.10

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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

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Theorem 5.6 Incenter Theorem

Theorem 5.7 Centroid Theorem

Theorem 5.8 Exterior Angle Inequality Theorem

Theorem 5.9

Theorem 5.10

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Theorem 5.11 Triangle Inequality Theorem

Theorem 5.12

Corollary 5.1

Theorem 5.13 SAS Inequality/Hinge Theorem

Theorem 5.14 SSS Inequality

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CHAPTER 6 QUADRILATERALS

Theorem 6.1 Interior Angle Sum Theorem

Theorem 6.2 Exterior Angle Sum Theorem

Theorems 6.3 - 6.6

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Theorem 6.7

Theorem 6.8

Theorems 6.9 – 6.12 Proving Parallelograms

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Theorem 6.13

Theorem 6.14

Theorems 6.15 – 6.17 Rhombus

Theorem 6.18 and 6.19 Isosceles Trapezoid

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Theorem 6.20

CHAPTER 7 Proportions and similarity

Postulate 7.1 Angle-Angle (AA) Similarity

Theorem 7.1 and 7.2

Theorem 7.3

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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

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Theorem 7.7 Proportional Perimeters Theorem

Theorem 7.8 – 7.10 Special Segments of Similar Triangles

Theorem 7.11 Angle Bisector Theorem

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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

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Theorem 8.6

Theorem 8.7

Theorem 8.8 Law of Sines

Theorem 8.9 Law of Cosines

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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

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Theorem 10.2

Theorem 10.3

Theorem 10.4

Theorem 10.5 Inscribed Angle Theorem

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Theorem 10.6

Theorem 10.7

Theorem 10.8

Theorem 10.9

Theorem 10.10

Theorem 10.11

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Theorem 10.12

Theorem 10.13

Theorem 10.14

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Theorem 10.15

Theorem 10.16

Theorem 10.17

CHAPTER 11 AREA OF POLYGONS AND CIRCLES

Postulate 11.1

Postulate 11.2

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CHAPTER 13 VOLUME

Theorem 13.1