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Transcript
Exam 2 Study Guide Chapter 3 (Sections 3.5-3.6) Plane Geometry Terms Linear Pair Supplementary Perpendicular Perpendicular Bisector Vertical Angles Congruence of Triangles Isosceles Triangle Postulates/Theorems Z-Theorem Crossbar Theorem and its converse Linear Pair Theorem Existence and Uniqueness of Perpendicular Bisector Vertical Angles Theorem SAS Isosceles Triangle Theorem Activities Draw pictures to illustrate terms and theorems Explain what needs to be shown to prove something is one of the terms listed Explain what conditions must hold to use a particular theorem Describe what results or conditions are guaranteed by a particular theorem Prove elementary results using terms and theorems Chapter 4 Neutral Geometry Terms Exterior Angle Remote Interior Angle Perpendiculars Dropping a Perpendicular Distance from a Point to a Line Foot of a Perpendicular Alternate Interior Angles Corresponding Angles Double Perpendicular Construction Quadrilateral Parallelogram Convex Quadrilateral Angle sum of Triangles and Quadrilaterals Similar Triangles Defect of triangles and quadrilaterals Rectangle Saccheri Quadrilaterals and their Properties Theorems Exterior Angle Theorem Existence and Uniqueness of Perpendiculars ASA, AAS, SSS Converse to Isosceles Triangle Theorem Hypotenuse-Leg Theorem Scalene Inequality Triangle Inequality Hinge Theorem Pointwise Characterization of Angle Bisector Pointwise Characterization of Perpendicular Bisector Alternate Interior Angles Theorem Corresponding Angles Theorem Existence of Parallels Corollary Saccheri-Legendre Theorem Theorem 4.6.8 Converse to Alt Int Ang Thm Euclid's Postulate V Statements #1 and 4 in Thm 4.7.3 Angle Sum Postulate Wallis's Postulate Activities Draw pictures to illustrate terms and theorems Explain what needs to be shown to prove something is one of the terms listed Explain what conditions must hold to use a particular theorem Describe what results or conditions are guaranteed by a particular theorem Identify which conditions will imply the Euclidean Parallel Postulate Identify and describe differences between Euclidean and hyperbolic geometries Identify which results hold for both Euclidean and hyperbolic geometries Fill in the justifications for a proof. Prove the triangle congruence Over → Lambert Quadrilaterals and their Properties Additivity of Defect Theorem 4.8.4 Lemma 4.8.6 Clairaut's Axiom Universal Hyperbolic Theorem theorems. Prove elementary results using terms and theorems
