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Proofs 2.5/2.6 Notes Using Proof In Algebra and Geometry and 2 column proofs Properties of Equality for Real Numbers Reflexive Symmetric Transitive Addition and Subtraction Multiplication and Division Substitution Distributive Now let’s look at how these properties from algebra can be used to discuss relationships between segments measures and also angle measures… Property Segments Angles Theorem Linear pair theorem If 2 angles form a linear pair, then they are supplementary Hypothesis Conclusion Congruent Supplements Theorem If 2 angles are supplementary to the same angle (or to 2 congruent angles), then the 2 angles are congruent. Right Angle congruence All right angles are congruent. Congruent Complements Theorem If 2 angles are complementary to the same angle (or to 2 congruent angles), then the 2 angles are congruent. Example 1: Name the property of equality that justifies each statement Statements a. If AB + BC = DE, then AB = DE b. c. If XY = PQ and XY = RS, then PQ = RS d. If e. If Reasons Example 2: Prove If (3x + 5)/2 = 7, then x = 3 Statements Reasons 1. The types of proofs we just constructed are called _______________________________________ OR __________________________________________ . Example 3: Justify the steps for the proof of If PR = QS, then PQ = RS Given: __________ Prove: ___________ Statements Reasons 1. PQ = QS 2. PQ + QR = PR QR + RS = QS 3. PQ +QR = QR +RS 4. PQ = RS 1 _____________________ 2 _____________________ 3 ____________________ 4 ____________________ Example 4: Justify the steps for the proof of: If Statements Reasons 1) 1) Given 2) mABD mDBC 90 2) 3) 3) Angle addition postulate 4) 5) mABC 90 4) 5) Definition of a right angle The Proof Process (p.112) Write the steps here. It will help you in the future I promise!