Algebraic Proofs and Intro to Geometric Proofs
 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 EqualityReflexive Property of EqualityTransitive Property of EqualitySubstitution Property of Equality 2.  Which property justifies the work from Step 1 to Step 2 below?Step 1:  5x + 9 = 16Step 2:  5x = 7Subtraction Property of EqualityMultiplication Property of EqualityDivision Property of Equality 3.  Which property justifies the work from Step 1 to Step 2 below?Step 1:  7m = 63Step 2:  m = 9Addition Property of EqualitySubtraction Property of EqualityDivision Property of Equality 4.  Which property justifies the work from Step 1 to Step 2 below?Step 1:  -8 + 6n = 4Step 2:  6n = 12Multiplication Property of EqualityAddition Property of EqualityDivision Property of Equality 5.  Which property justifies the work from Step 1 to Step 2 below?Step 1:  -x = 15Step 2:  x = -15Addition Property of EqualitySubtraction Property of EqualityDivision 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 ) = 362.   4x - 12 = 363.   4x = 484.   x = 12STEPSAddition Property of Equality?Division Property of Equality?Distributive Property?REASONSGivenReflexive 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 = 243.   -6x = 121.  -6( x - 2 ) = 244.   x = -2STEPSSubtraction Property of =?Distributive Property?Division Property of =?REASONSAssociative 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 Congruence8.  Which property is used to justify the following statement?Symmetric Property of CongruenceSubstitution Property of CongruenceReflexive Property of CongruenceΔABC ≅ ΔABC 9.  Which property is used to justify the following statement?Symmetric Property of CongruenceReflexive Property of CongruenceTransitive Property of CongruenceSubstitution Property of CongruenceIf ∠A≅∠B and ∠B≅∠C, then ∠A≅∠C. 10.  Which property is used to justify the following statement?Symmetric Property of CongruenceTransitive Property of CongruenceReflexive Property of CongruenceSubstitution 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∡CAB3.   2x + 4x + 6 = 724.   6x + 6 = 721. m∡CAB = 72º5.   6x = 666.   x = 11STEPSSubstitution Property of =?Subtraction Property of =?Angle Addition Postulate?Division Property of =?REASONSSimplify?Given?Transitive Property of =?not used:
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