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In this activity, you will work on algebraic proofs and you will learn about geometric proofs. Proving things are true is a very important skill to have as a mathematician! Be thinking about the "steps" in a proof. Also be thinking about how to justify each step.What property of numbers, congruence, orequality can be applied as reasons in your proof? 1. Which property is used to justify the following statement? Let a = 5 and b = 16. 2ab = 2(5)(16) = 160. Symmetric Property of Equality Reflexive Property of Equality Transitive Property of Equality Substitution Property of Equality 2. Which property justifies the work from Step 1 to Step 2 below? Step 1: 5x + 9 = 16 Step 2: 5x = 7 Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality 3. Which property justifies the work from Step 1 to Step 2 below? Step 1: 7m = 63Step 2: m = 9 Addition Property of Equality Subtraction Property of Equality Division Property of Equality 4. Which property justifies the work from Step 1 to Step 2 below? Step 1: -8 + 6n = 4Step 2: 6n = 12 Multiplication Property of Equality Addition Property of Equality Division Property of Equality 5. Which property justifies the work from Step 1 to Step 2 below? Step 1: -x = 15Step 2: x = -15 Addition Property of Equality Subtraction Property of Equality Division Property of Equality 6. Fill in the missing parts of the proof by dragging the justifications to the correct step of the proof. 1. 4( x - 3 ) = 36 2. 4x - 12 = 36 3. 4x = 48 4. x = 12 STEPS Addition Property of Equality ? Division Property of Equality ? Distributive Property ? REASONS Given Reflexive Property of = ? not used: 7. Fill in the missing parts of the proof by dragging the justifications to the correct step of the proof. 2. -6x + 12 = 24 3. -6x = 12 1. -6( x - 2 ) = 24 4. x = -2 STEPS Subtraction Property of = ? Distributive Property ? Division Property of = ? REASONS Associative Property of = ? Given ? not used: Geometric Proofs are related to Algebraic Proofs, in the sensethat every statement should be justified by a reason. All statements in a geometric proof work toward an "end goal",just like the "end goal" of solving an equation is finding the valueof the variable that makes the equation true. In a geometric proof, the statements and reasons will be relatedto known definitions, theorems, postulates, and properties ofcongruence. Transitive Property of Congruence 8. Which property is used to justify the following statement? Symmetric Property of Congruence Substitution Property of Congruence Reflexive Property of Congruence ΔABC ≅ ΔABC 9. Which property is used to justify the following statement? Symmetric Property of Congruence Reflexive Property of Congruence Transitive Property of Congruence Substitution Property of Congruence If ∠A≅∠B and ∠B≅∠C, then ∠A≅∠C. 10. Which property is used to justify the following statement? Symmetric Property of Congruence Transitive Property of Congruence Reflexive Property of Congruence Substitution Property of Congruence If EF ≅ HG, then HG ≅ EF. TRY THIS!11. Complete the proof by dragging the reasons to the correct step of the proof. In the diagram, m∠CAB = 72º. Solve for "x". 2. m∡CAD+m∡DAB=m∡CAB 3. 2x + 4x + 6 = 72 4. 6x + 6 = 72 1. m∡CAB = 72º 5. 6x = 66 6. x = 11 STEPS Substitution Property of = ? Subtraction Property of = ? Angle Addition Postulate ? Division Property of = ? REASONS Simplify ? Given ? Transitive Property of = ? not used: |