Presentation on theme: "Chapter 2 Properties from Algebra"— Presentation transcript:
1 Chapter 2 Properties from Algebra Objective: To connect reasoning in Algebra & Geometry
2 ObjectivesReview properties of equality and use them to write algebraic and geometric proofs.Identify properties of equality and congruence.
3 In Geometry you accept postulates & properties as true. You use Deductive Reasoning to prove other statements.In Algebra you accept the Properties of Equality as true also.
4 Algebra Properties of Equality Addition Property:If a = b, then a + c = b + cSubtraction Property:If a = b, then a – c = b – cMultiplication Property:If a = b, then a • c = b • cDivision Property:If a = b, then a/c = b/c (c ≠ 0)
5 More Algebra Properties Reflexive Property:a = a (A number is equal to itself)Symmetric Property:If a = b, then b = aTransitive Property:If a = b & b = c, then a =c
6 2 more Algebra Properties Substitution Properties: (Subs.)If a = b, then “b” can replace “a” anywhereDistributive Properties:a(b +c) = ab + ac
7 A proof is an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true.An important part of writing a proof is giving justifications to show that every step is valid.
8 Example 1: Algebra Proof 3x = 15x = 55 = x1. Given Statement2. Subtr. Prop3. Division Prop4. Symmetric Prop
10 Example 3: Segment Addition Proof Given: AB = 4 + 2x. BC = 15 – x Example 3: Segment Addition Proof Given: AB = 4 + 2x BC = 15 – x AC = 21 Prove: x = 2A15 – xC4 + 2xBStatementsAB=4+2x, BC=15 – x, AC=21AC = AB + BC21 = 4 + 2x + 15 – x21 = 19 + x2 = xx = 2ReasonsGivenSegment Add. Prop.Subst. Prop.Combined Like Term.Subtr. Prop.Symmetric Prop.
11 You learned in Chapter 1 that segments with equal lengths are congruent and that angles with equal measures are congruent. So the Reflexive, Symmetric, and Transitive Properties of Equality have corresponding properties of congruence.
12 Geometry Properties of Congruence Reflexive Property: AB ABA ASymmetric Prop: If AB CD, then CD ABIf A B, then B ATransitive Prop:If AB CD and CD EF, then AB EFIF A B and B C, then A C
14 What did I learn Today? TU XY and XY AB, then TU AB Reflexive Name the property for each of the following steps.P Q, then Q PSymmetric PropTU XY and XY AB, then TU ABTransitive PropDF DFReflexive