Daily Warm Up Quiz Mrs. McConaughyGeometry1 I. Complete each theorem below: 1.Vertical angles are ________________________________ 2.Linear pairs of angles are ____________________________ 3.If two angles are congruent and supplementary, then ________ _______________________________________________. II. Define: Complementary angle:___________________________________ Supplementary angle; ___________________________________ III. Given the following diagram, name A.All linear pairs of angles ____________________________ B.All vertical angle pairs ____________________________

Mrs. McConaughyGeometry2 Introduction to Proof, Part 1 During this lesson, you will:  Identify premises for geometric argument  Write simple proofs using Properties of Algebra & Properties of Equality

Mrs. McConaughyGeometry3 Premises for Geometric Proof 1.Definitions and undefined terms 2.Properties of algebra, equality, and congruence 3.Postulates of geometry 4.Previously accepted or proven geometric theorems

Mrs. McConaughyGeometry4 Matching Review: Properties of Algebra Column A __ Commutative Property of Addition __ Commutative Property of Multiplication __ Associative Property of Addition __ Associative Property of Multiplication __Distributive Property Column B a.a + b = b + a b. (a + b) + c = a + (b + c) c. (ab)c = a(bc) d. ab = ba e. a (b + c) = ab + ac a d b c e

Mrs. McConaughyGeometry5 Matching Review: Properties of Equality __Reflexive Property of Equality __Symmetric Property of Equality __Addition Property of Equality __Subtraction Property of Equality __Multiplication Property of Equality __Division Property of Equality 1.a = a 2.If a = b then b = a. 3. If a = b, then a + c = b + c 4. If a = b, then a * c = b * c 5. If a = b, then a - c = b – c 6. If a = b, then a / c = b / c (provided c ≠ 0)

Mrs. McConaughyGeometry6 Writing Simple Algebraic Proofs Using Properties of Algebra & Equality You use properties of algebra and equality to solve equations. When you solve an equation, you are writing an algebraic proof. Each step can be supported by a property.

Mrs. McConaughyGeometry7 Example A: Given: 5x – 12 = 3 (x + 2) Prove: x = 9 StatementReason

Mrs. McConaughyGeometry8 Example B: If ax + b = c, then x = (c-b)/a; a ≠ 0. Given: Prove: ax + b = cx = (c-b)/a StatementReason

Mrs. McConaughyGeometry9 Final Checks For Understanding If each statement in the first column is given information, for the corresponding conclusion? Given Conclusion RT + LM = 19; LM = 7 RT= 12 m AB = 25 2 (mAB) = 50 AZ = 26 AZ/2 = 13

Mrs. McConaughyGeometry10 Homework Assignment #1 Writing Simple Algebraic Proofs Supplemental WS, plus page 91-92: 1, 2 3,