ࡱ>  y'bjbj ccyjj<:.00000***?:A:A:A:A:A:A:$;>xe:*'***e:00 z:333*j00?:3*?:33:7,80Փ#+ #8 +::0:-8R?-+?8?8**3*****e:e:3***:****?*********j : GEOMETRY POSTULATES, PROPERTIES AND THEOREMS Postulate 1-1  Postulate 1-2  Postulate 1-3  Postulate 1-4  Postulate 1-5 Ruler Postulate  Definition of Congruent Segments Postulate 1-6 Segment Addition Postulate Definition of Midpoint Definition of Perpendicular Lines Definition of Perpendicular Bisector  Postulate 1-7 Protractor Postulate Postulate 1-8 Angle Addition Postulate Definition of Congruent Angles Definition of Angle Bisector Distance Formula Midpoint FormulaPerimeter and Area of a SquarePerimeter and Area of a RectangleCircumference and Area of a CirclePostulate 1-9 Postulate 1-10  Definition of a Conditional  Venn Diagram Definition of a Converse Definition of a Biconditional Negation of Statements Definition of an Inverse Definition of a Contrapositive Equivalent Statements Writing an Indirect Proof 1. Assume the opposite (negation) of what you want to prove. 2. Show that this assumption leads to a contradiction. 3. Conclude that Therefore, the assumption must be false and that what you want to prove must be true. Law of Detachment Law of Syllogism Addition Property of Equality Subtraction Property of Equality Multiplication Property of Equality  Division Property of Equality  Reflexive Property of Equality  Symmetric Property of Equality  Transitive Property of Equality Substitution Property Distributive Property of Equality   Reflexive Property of Congruence Symmetric Property of Congruence  Transitive Property of Congruence Definition of Adjacent Angles Definition of Vertical Angles  Theorem 2-1 Vertical Angles Theorem Definition of Supplementary Definition of Complementary Theorem 2-2 Congruent Supplements Theorem Theorem 2-3 Congruent Complements Theorem Theorem 2-4 Theorem 2-5  Postulate 3-1 Corresponding Angles Postulate Theorem 3-1 Alternate Interior Angles Theorem Theorem 3-2 Same-Side Interior Angles Theorem Postulate 3-2 Converse of the Corresponding Angles Postulate Theorem 3-3 Converse of the Alternate Interior Angles Theorem Theorem 3-4 Converse of the Same-Side Interior Angles TheoremTheorem 3-5 Theorem 3-6 Theorem 3-7 Triangle Sum Theorem Theorem 3-8 Triangle Exterior Angle Theorem Classifying Triangles By SidesClassifying Triangles By Angles Theorem 3-9 Polygon Angle Sum Theorem Each Interior Angle of a REGULAR PolygonTheorem 3-10 Polygon Exterior Angle Sum Theorem Each Exterior Angle of a REGULAR PolygonSlope-Intercept Form of a Line Standard Form of a Line Point-Slope Form of a Line Summary Horizontal Lines Summary Vertical Lines Summary Slopes of Parallel Lines Summary Slopes of Perpendicular Lines  Theorem 4-1 Congruent Angles of Triangles Postulate 4-1 Side-Side-Side Postulate (SSS) Postulate 4-2 Side-Angle-Side Postulate (SAS) Postulate 4-3 Angle-Side-Angle Postulate (ASA) Theorem 4-2 Angle-Angle-Side Theorem (AAS) Congruent Triangles ( Congruent Parts CPCTC Theorem 4-3 Isosceles Triangle Theorem Corollary to Theorem 4-3 Equilateral ( Equiangular Theorem 4-4 Converse of Isosceles Triangle Theorem Corollary to Theorem 4-4 Equiangular ( Equilateral Theorem 4-5 Isosceles Triangle Bisector Theorem  Theorem 4-6 Hypotenuse-Leg Theorem (HL)   Theorem 5-1 Triangle Mid-segment Theorem Theorem 5-2 Perpendicular Bisector Theorem Theorem 5-3 Converse of the Perpendicular Bisector Theorem Theorem 5-4 Angle Bisector Theorem Theorem 5-5 Converse of the Angle Bisector Theorem  Theorem 5-6 Circumcenter Theorem 5-7 Incenter Theorem 5-8 Centroid Theorem 5-9 Orthocenter  Comparison Property of Inequality Corollary to the Triangle Exterior Angle Theorem Theorem 5-10 Theorem 5-11 Theorem 5-12 Triangle Inequality Theorem Definition of a Parallelogram  Definition of a Rhombus Definition of a Rectangle Definition of a Square Definition of a Kite Definition of a Trapezoid Definition of an Isosceles Trapezoid Theorem 6-1 Theorem 6-2 Consecutive Angles of a Parallelogram Theorem 6-3 Theorem 6-4 Theorem 6-5 Theorem 6-6 Theorem 6-7 Theorem 6-8 Theorem 6-9 Theorem 6-10 Theorem 6-11 Theorem 6-12 Theorem 6-13  Theorem 6-14 Theorem 6-15 Theorem 6-16  Theorem 6-17  Theorem 6-18 Trapezoid Midsegment Theorem (Section 6.7) R A  M N T PTheorem 7-1 Area of a Rectangle Area of a Square Theorem 7-2 Area of a Parallelogram Theorem 7-3 Area of a Triangle Herons Formula Theorem 7-4 Pythagorean Theorem Theorem 7-5 Converse of the Pythagorean TheoremTheorem 7-6 Theorem 7-7 Theorem 7-8 45(-45(-90( Triangle Theorem Theorem 7-9 30(-60(-90( Triangle Theorem Theorem 7-10 Area of a Trapezoid   Theorem 7-11 Area of a Rhombus or a Kite Theorem 7-12 Area of a Regular Polygon Postulate 7-1 Arc Addition Postulate Theorem 7-13 Circumference of a Circle Theorem 7-14 Arc Length Theorem 7-15 Area of a Circle Theorem 7-16 Area of a Sector of a Circle Segment of a circle  Properties of Proportions  Algebra Review: Quadratic Formula  Defintion of Similarity  The Golden Ratio Postulate 8-1 Angle-Angle Similarity (AA~) Theorem 8-1 Side-Angle-Side Similarity Thm. (SAS~) Theorem 8-2 Side-Side-Side Similarity Thm. (SSS~)  Theorem 8-3  Definition of Geometric Mean  Corollary 1 to Theorem 8-3   Corollary 2 to Theorem 8-3 Theorem 8-4 Side-Splitter Theorem Corollary to Theorem 8-4 Theorem 8-5 Triangle-Angle-Bisector Theorem Theorem 8-6 Perimeters and Areas of Similar Figures  CHAPTER 9 Tangent Ratio  Sine Ratio  Cosine Ratio  Angles of Elevation and Depression Vectors  Finding Vector Coordinates   Finding Vector Magnitude and Direction  Property Adding Vectors  Polyhedron Face Edge Vertex Eulers Formula Net Cross Section  Prisms Theorem 10-1 Lateral and Surface Areas of a Prism Theorem 10-2 Lateral and Surface Areas of a Cylinder Surface Area of a Rectangular Prism Lateral and Surface Area of a Cube  Pyramids Theorem 10-3 Lateral and Surface Areas of a Regular PyramidTheorem 10-4 Lateral and Surface Areas of a Cone Theorem 10-5 Cavalieris Principle Theorem 10-6 Volume of a Prism Theorem 10-7 Volume of a Cylinder  Theorem 10-8 Volume of a Pyramid  Theorem 10-9 Volume of a Cone  Theorem 10-10 Surface Area of a Sphere  Theorem 10-11 Volume of a Sphere Theorem 10-12 Areas and Volumes of Similar Solids  Tangents  Theorem 11-1  Theorem 11-2  Theorem 11-3  Theorem 11-4  Theorem 11-5  Theorem 11-6  Theorem 11-7  Theorem 11-8  Theorem 11-9 Inscribed Angle Theorem  Corollary 1 to the Inscribed Angle Theorem  Corollary 2 to the Inscribed Angle Theorem  Corollary 3 to the Inscribed Angle Theorem  Theorem 11-10  Theorem 11-11 (1)  Theorem 11-11 (2)  Theorem 11-12 (Lengths of Segments)    Theorem 11-13 Equation of a Circle  Transformations  Reflections  Translations  Composition  Rotations  Theorem 12-1  Theorem 12-2  Theorem 12-3 Theorem 12-4 Fundamental Theorem of Isometries Theorem 12-5 Isometry Classification Theorem  Symmetry  Tessellations  Theorem 12-6  Theorem 12-7  Dilations  -.BCTWXilm d e 3 4 5 7 V X Y [ z | } ~  h0K6] hE 6]h`(h0K hh 6]hh h&jhoUmHnHuhohwJ h CJh hq hE CJhE 5CJ\hE @-.<=>?@ABCQRSsvkd$$Ifl0P0*"064 layt $If $$Ifa$$a$ STUVWXfghijklwww $$Ifa$vkd$$Ifl0P0*"064 layt  $Ifgdq 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