2-5: Verifying Segment Relationships

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Presentation transcript:

2-5: Verifying Segment Relationships Expectations: L4.3.1: Know the basic structure of an “If, then” proof. G1.1.6: Recognize Euclidean geometry as an axiom system. Know the key axioms and understand the meaning of and distinguish between undefined terms (e.g., point, line, and plane), axioms, definitions, and theorems. 4/17/2017 2-5: Verifying Segment Relationships

Equivalence Property of Congruence Theorem a. Congruence of segments is reflexive AB  b. Congruence of segments is symmetric: If AB  CD, then c. Congruence of segments is transitive: If AB  CD and CD  EF, then 4/17/2017 2-5: Verifying Segment Relationships

Parts of a Geometric Proof a. State the theorem (may already be done for you). b. State the given (hypothesis) and what you are trying to prove (conclusion). c. Draw a diagram. d. Start with the given and deduce statements until you reach the conclusion. 4/17/2017 2-5: Verifying Segment Relationships

Prove the Symmetric Property of Congruence State the theorem: What is the given? What must we prove? 4/17/2017 2-5: Verifying Segment Relationships

2-5: Verifying Segment Relationships Complete the Proof 4/17/2017 2-5: Verifying Segment Relationships

2-5: Verifying Segment Relationships Given: P, Q and S are collinear Prove: PQ = PS – QS P Q S 4/17/2017 2-5: Verifying Segment Relationships

2-5: Verifying Segment Relationships 4/17/2017 2-5: Verifying Segment Relationships

2-5: Verifying Segment Relationships Jerry stated that squaring a number always results in a positive result. Which of the following numbers is a counterexample to Jerry’s statement? -3 .-75 -½ 1⅓ 4/17/2017 2-5: Verifying Segment Relationships

2-5: Verifying Segment Relationships Complete Study Guide/Practice 2-5. Finish as homework. 4/17/2017 2-5: Verifying Segment Relationships

2-5: Verifying Segment Relationships What is the negation of the statement, “No squares are triangles?” all squares are triangles all triangles are squares no triangles are squares there exists at least one square that is a triangle. There exists at least one triangle that is a square. 4/17/2017 2-5: Verifying Segment Relationships

2-5: Verifying Segment Relationships Assignment pages 104-105, # 15-31 (odds), 37-45 (odds). 4/17/2017 2-5: Verifying Segment Relationships