2.1 Demonstrative Geometry Proofs (page 46) A proof or demonstration is the process of deductive reasoning where the truth of a theorem or the correctness of a construction is established Theorem – a statement not self-evident but proved by a chain of reasoning (Example on page 46) Construction – A figure that satisfies certain given conditions and is drawn without instruments of measurement (Example on page 46) Deductive reasoning is a process where the truth of a given statement follows previously mentioned statements known to be true. (Example on page 46)

2.1 Demonstrative Geometry Proofs cont. (page 46) Deductive reasoning examples All oranges are fruits, All fruits grow on trees, Therefore, all oranges grow on trees. Johnny is a bachelor, All bachelors are single, Hence, Johnny is single. Action: In your groups create an example using deductive reasoning to draw a conclusion

2.1 Demonstrative Geometry Proofs cont. (page 46) Four parts of the formal demonstration of a theorem in geometry: Given (hypothesis): a statement of beginning facts about lines, angles, figures, etc to be used Prove (conclusion): a statement of what is to be shown true Analysis: planning and reasoning to discover how to solve a proof Proof: logically arranged steps leading to the conclusion, with each step based on one of the following: The given information, a definition, an axiom, a postulate or a theorem

2.2 Triangles Proved Congruent by S.A.S. (page 47) Theorem 1: Two triangles are congruent if two sides and the included angles of one are equal respectively to two sides and the included angle of the other (Side Angle Side Theorem S.A.S.). A corollary is another geometric statement that is easily deduced from the given theorem just proved. Corollary 1 – 1: Two right triangles are congruent if the two legs of one triangle are equal respectively to the two legs of the other (Leg- Leg Theorem L.L.). Once we know that two triangles are congruent, we know that all corresponding parts are congruent. This is called corresponding parts of congruent triangles are equal (C.P.C.T.E.).

2.3 Triangles Proved Congruent by A.S.A. (pages 50 - 51) Theorem 1: Two triangles are congruent if two angles and the included side of one triangle are equal respectively to two angles and the included side of another (Angle Side Angle Theorem A.S.A.). The analysis step is a pre-proof planning step that can help solve proofs by guiding your thinking. Corollary 2 – 1: Two right triangles are congruent if the right angle, an acute angle and the included side of one triangle are equal respectively to the right angle, an acute angle the included side of another triangle. (Leg-Acute Angle Theorem L.A.).