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Download Geometry – Definitions, Postulates, and Theorems for Chapters 1-6
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Geometry – Definitions, Postulates, and Theorems for Chapters 1-6 All of these terms are important; many of them are used in proofs. However, I’ve bolded the terms that I think are especially important to know for filling in justification in proofs. Chapter 1 Point Line Plane Segment Endpoint Ray Opposite Rays Collinear Noncollinear Coplanar Ruler Postulate Segment Addition Postulate Midpoint Segment Bisector Congruent segments Angle Vertex Interior of an angle Exterior of an angle Protractor Postulate Acute angle Right angle Obtuse angle Straight angle Congruent angles Angle Addition Postulate Angle bisector Adjacent angles Linear pair Complementary angles Supplementary angles Vertical angles Perimeter Area Diameter, Radius, Circumference Coordinate plane Legs Hypotenuse Midpoint Formula Distance Formula Pythagorean Theorem Chapter 2 Inductive reasoning Conjecture Counterexample Conditional statements Hypothesis, Conclusion Truth Value Converse Inverse Contrapositive Logically equivalent statements Deductive reasoning Law of detachment Law of Syllogism Biconditional statements Polygon Triangle Quadrilateral Properties of Equality and Congruence -Addition -Subtraction -Multiplication -Division -Reflexive -Symmetric -Transitive -Substitution Linear Pair Theorem Congruent Supplements Theorem Right angle Congruence Theorem Congruent Complements Theorem Common Segments Theorem Vertical Angles Theorem Congruent Angles Supplementary → Right Angles Chapter 3 Parallel, Perpendicular, and Skew Lines Parallel Planes Transversal Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Same-Side Interior Angles Corresponding Angles Postulate (and Converse) Alternate Interior Angles Theorem (and Converse) Alternate Exterior Angles Theorem (and Converse) Same-Side Interior Angles Theorem (and Converse) Parallel Postulate Perpendicular Bisector and the distance from a point to a line Two intersecting lines form linear pair of congruent angles → lines Perpendicular Perpendicular Transversal Theorem 2 lines perpendicular to same line → Lines parallel Rise, Run, Slope Slope – Parallel Lines Theorem Slope – Perpendicular Lines Theorem Eq – Point-Slope Form Eq – Slope-Intercept Form Chapter 4 Acute Triangle Equiangular Triangle Right Triangle Obtuse Triangle Equilateral Triangle Isosceles Triangle Scalene Triangle Triangle Sum Theorem Exterior Angle Theorem Third Angles Theorem Corresponding angles/sides Congruent Polygons SSS, SAS, ASA, AAS, HL, CPCTC Coordinate Proof Isosceles Triangle Theorem (and Converse) Equilateral/Equiangular Triangle Theorem Chapter 5 Equidistant Perpendicular Bisector Theorem (and Converse) Angle Bisector Theorem (and Converse) Concurrent, Point of Concurrency Circumcenter Theorem Incenter Theorem Inscribed circle Median of a triangle Centroid Theorem Altitude of a triangle Orthocenter of a triangle Triangle Midsegment Theorem In triangle longer side opposite larger angle (and converse) Triangle Inequality Theorem Hinge Theorem (and Converse) Chapter 6 Regular, Concave, Convex Polygons Polygon Exterior Angle Theorem Parallelogram → opposite sides congruent Parallelogram → opposite angles congruent Parallelogram → consecutive angles supp. Parallelogram → diagonals bisect each other Quad. with 1 pair opposite sides parallel and congruent → Parallelogram Quad. with opposite sides congruent → Parallelogram Quad. with opposite angles congruent → Parallelogram Quad. with angles supp. to consecutive angles → Parallelogram Quad with diagonals bisecting each other → Parallelogram Rectangle → Parallelogram Rectangle → Diagonals congruent Rhombus → Parallelogram Rhombus → Diagonals perpendicular Rhombus → Each diagonal bisects opposite angles Parallelogram with one right angle → Rectangle Parallelogram with diagonals congruent → Rectangle Parallelogram with one pair of consecutive sides congruent → rhombus Parallelogram with diagonals perpendicular → rhombus Parallelogram with diagonals bisecting opposite angles → rhombus Kite → diagonals perpendicular Kite → one pair opposite angles congruent Isosceles trapezoid → base angles congruent Trapezoid with pair of base angles congruent → Isosceles trapezoid Isosceles trapezoid ↔ diagonals are congruent Trapezoid Midsegment theorem
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