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Name_____________________________________________________ Period_____ Geometry, Semester 1 Chapter 1: CONCEPTS Undefined terms (2) Point ___________________________________________________________________________________ Line ___________________________________________________________________________________ Plane ___________________________________________________________________________________ Defined terms (3) Segment ___________________________________________________________________________________ Endpoints ___________________________________________________________________________________ Ray ___________________________________________________________________________________ Midpoint Formula (16) ______________________________________________________________________________________ Distance Formula (17) ______________________________________________________________________________________ Identify Polygons (42) ______________________________________________________________________________________ Formulas for (49) Perimeter ___________________________________________________________________________________ Area ___________________________________________________________________________________ Circumference ___________________________________________________________________________________ POSTULATES Ruler Postulate (9) ______________________________________________________________________________________ Segment Addition Postulate (10) ______________________________________________________________________________________ Protractor Postulate (24) ______________________________________________________________________________________ Angle Addition Postulate (25) ______________________________________________________________________________________ 1 Chapter 2: CONCEPTS Perpendicular Lines (81) ______________________________________________________________________________________ Laws of Logic (87) Law of Detachment ___________________________________________________________________________________ Law of Syllogism ___________________________________________________________________________________ PROPERTIES Addition Property of Equality (105) ______________________________________________________________________________________ Subtraction Property of Equality (105) ______________________________________________________________________________________ Multiplication Property of Equality (105) ______________________________________________________________________________________ Division Property of Equality (105) ______________________________________________________________________________________ Substitution Property of Equality (105) ______________________________________________________________________________________ Distributive Property (106) ______________________________________________________________________________________ Reflexive Property of Equality (107) Real Numbers ___________________________________________________________________________________ Segment Length ___________________________________________________________________________________ Angle Measure ___________________________________________________________________________________ Symmetric Property of Equality (107) Real Numbers ___________________________________________________________________________________ Segment Length ___________________________________________________________________________________ Angle Measure ___________________________________________________________________________________ Transitive Property of Equality (107) Real Numbers ___________________________________________________________________________________ Segment Length ___________________________________________________________________________________ Angle Measure ___________________________________________________________________________________ 2 POSTULATES Point, Line and Plane Postulates (96) 5 ___________________________________________________________________________________ 6 ___________________________________________________________________________________ 7 ___________________________________________________________________________________ 8 ___________________________________________________________________________________ 9 ___________________________________________________________________________________ 10 ___________________________________________________________________________________ 11 ___________________________________________________________________________________ Linear Pair Postulate (126) ______________________________________________________________________________________ THEOREMS Congruence of Segments (113) Reflexive ___________________________________________________________________________________ Symmetric ___________________________________________________________________________________ Transitive ___________________________________________________________________________________ Congruence of Angles (113) Reflexive ___________________________________________________________________________________ Symmetric ___________________________________________________________________________________ Transitive ___________________________________________________________________________________ Right Angle Congruence Theorem (124) ______________________________________________________________________________________ Congruent Supplements Theorem (125) ______________________________________________________________________________________ Congruent Complements Theorem (125) ______________________________________________________________________________________ Vertical Angles Congruence Theorem (126) ______________________________________________________________________________________ 3 Chapter 3: CONCEPTS Angles formed by Transversals (149) Corresponding Angles ___________________________________________________________________________________ Alternate Interior Angles ___________________________________________________________________________________ Alternate Exterior Angles ___________________________________________________________________________________ Consecutive Interior Angles ___________________________________________________________________________________ Slopes of Lines in a Coordinate Plane (171) Negative ___________________________________________________________________________________ Positive ___________________________________________________________________________________ Zero (horizontal) ___________________________________________________________________________________ Undefined (vertical) ___________________________________________________________________________________ POSTULATES Chapter 3: Parallel Postulate (148) ______________________________________________________________________________________ Perpendicular Postulate (148) ______________________________________________________________________________________ Corresponding Angles Postulate (154) ______________________________________________________________________________________ Corresponding Angles Converse (161) ______________________________________________________________________________________ Slopes of Parallel Lines (172) ______________________________________________________________________________________ Slopes of Perpendicular Lines (172) ______________________________________________________________________________________ 4 THEOREMS Alternate Interior Angles Theorem (155) ______________________________________________________________________________________ Alternate Exterior Angles Theorem (155) ______________________________________________________________________________________ Consecutive Interior Angles Theorem (155) ______________________________________________________________________________________ Alternate Interior Angles Converse (162) ______________________________________________________________________________________ Alternate Exterior Angles Converse (162) ______________________________________________________________________________________ Consecutive Interior Angles Converse (162) ______________________________________________________________________________________ Transitive Property of Parallel Lines (164) ______________________________________________________________________________________ Theorem 3.8 (190) ______________________________________________________________________________________ Theorem 3.9 (190) ______________________________________________________________________________________ Theorem 3.10 (191) ______________________________________________________________________________________ Perpendicular Transversal Theorem (192) ______________________________________________________________________________________ Lines Perpendicular to a Transversal Theorem (192) ______________________________________________________________________________________ 5 Chapter 4: CONCEPTS Classify Triangles by Sides (217) Scalene ___________________________________________________________________________________ Isosceles ___________________________________________________________________________________ Equilateral ___________________________________________________________________________________ Classify Triangles by Angles (217) Acute ___________________________________________________________________________________ Right ___________________________________________________________________________________ Obtuse ___________________________________________________________________________________ Equiangular ___________________________________________________________________________________ Coordinate Notation for a Translation (273) ______________________________________________________________________________________ Coordinate Notation for a Reflection (273) ______________________________________________________________________________________ PROPERTIES Reflexive Property of Triangle Congruence (228) ______________________________________________________________________________________ Symmetric Property of Triangle Congruence (228) ______________________________________________________________________________________ Transitive Property of Triangle Congruence (228) ______________________________________________________________________________________ POSTULATES Side-Side-Side (SSS) Congruence Postulate (234) ______________________________________________________________________________________ Side-Angle-Side (SAS) Congruence Postulate (240) ______________________________________________________________________________________ Angle-Side-Angle (ASA) Congruence Postulate (249) ______________________________________________________________________________________ 6 THEOREMS Triangle Sum Theorem (218) ______________________________________________________________________________________ Exterior Angle Theorem (219) ______________________________________________________________________________________ Corollary to the Triangle Sum Theorem (220) ______________________________________________________________________________________ Corresponding Parts of Congruent Triangles are Congruent (CPCTC) (225) ______________________________________________________________________________________ Third Angles Theorem (227) ______________________________________________________________________________________ Hypotenuse-Leg (HL) Congruence Theorem (241) ______________________________________________________________________________________ Angle-Angle-Side (AAS) Congruence Theorem (249) ______________________________________________________________________________________ Base Angles Theorem (264) ______________________________________________________________________________________ Converse of Base Angles Theorem (264) ______________________________________________________________________________________ Corollary to Base Angles Theorem (265) ______________________________________________________________________________________ Corollary to Converse of Base Angles Theorem (265) ______________________________________________________________________________________ 7 Chapter 5: THEOREMS Mid-Segment Theorem (295) ______________________________________________________________________________________ Perpendicular Bisector Theorem (303) ______________________________________________________________________________________ Converse of the Perpendicular Bisector Theorem (303) ______________________________________________________________________________________ Concurrency of Perpendicular Bisectors of a Triangle Theorem (305) ______________________________________________________________________________________ Angle Bisector Theorem (310) ______________________________________________________________________________________ Converse of the Angle Bisector Theorem (310) ______________________________________________________________________________________ Concurrency of Angle Bisectors of a Triangle Theorem (312) ______________________________________________________________________________________ Concurrency of Medians of a Triangle Theorem (319) ______________________________________________________________________________________ Concurrency of Altitudes of a Triangle Theorem (320) ______________________________________________________________________________________ Theorem 5.10 (328) ______________________________________________________________________________________ Theorem 5.11 (328) ______________________________________________________________________________________ Triangle Inequality Theorem (330) ______________________________________________________________________________________ Hinge Theorem (335) ______________________________________________________________________________________ Converse of the Hinge Theorem (335) ______________________________________________________________________________________ 8 Chapter 6: CONCEPTS Geometric Mean (359) ______________________________________________________________________________________ Corresponding Lengths in Similar Polygons (375) ______________________________________________________________________________________ Coordinate Notation for a Dilation (409) ______________________________________________________________________________________ PROPERTIES Cross Products Property (358) ______________________________________________________________________________________ Reciprocal Property (364) ______________________________________________________________________________________ POSTULATES Angle-Angle Similarity Postulate (381) ______________________________________________________________________________________ THEOREMS Perimeters of Similar Polygons (374) ______________________________________________________________________________________ Side-Side-Side Similarity Theorem (388) ______________________________________________________________________________________ Side-Angle-Side Similarity Theorem (390) ______________________________________________________________________________________ Triangle Proportionality Theorem (397) ______________________________________________________________________________________ Converse of the Triangle Proportionality Theorem (397) ______________________________________________________________________________________ Theorem 6.6 (398) ______________________________________________________________________________________ Theorem 6.7 (398) ______________________________________________________________________________________ 9 Chapter 7: CONCEPTS Pythagorean Triples and their multiples (435) ______________________________________________________________________________________ THEOREMS Pythagorean Theorem (433) ______________________________________________________________________________________ Converse of the Pythagorean Theorem (441) ______________________________________________________________________________________ Theorem 7.3 (442) ______________________________________________________________________________________ Theorem 7.4 (442) ______________________________________________________________________________________ Theorem 7.5 (449) ______________________________________________________________________________________ Geometric Mean (Altitude) Theorem (453) ______________________________________________________________________________________ Geometric Mean (Leg) Theorem (453) ______________________________________________________________________________________ 10