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Notes: 2-5 Reasoning in Algebra and Geometry Name_____________________ Date_______ Per__ Property Symbols Symmetric Property of Equality Words You can ________ the same number to each side of an equation You can __________ the same number from each side of an equation. You can ___________ by the same number on each side of an equation. You can __________ each side an equation by the same number. You can ______________ a part of an expression with an equivalent value. Any value is __________ to itself. Any geometric object is ___________ to itself. You can change the order of an ____________ Symmetric Property of Congruence You can change the order of a _____________ If Q R, then R Q. statement. Addition Property Subtraction Property Multiplication Property Division Property Substitution Reflexive Property of Equality Reflexive Property of Congruence Transitive Property of Equality Transitive Property of Congruence If x = 2, then x + 2 = 4. If y = 8, then y – 3 = 5. If z = 2, then 5z = 10. If 6m = 12, then m = 2. If 3x + 5 = 3 and x = 2, then 3(2) + 5 = 3. AB = AB Z Z If XY = ZA, then ZA = XY If two values are _________ to a third If KL = MN and MN = TR, then KL = TR value, then they are equal to each other. If two values are congruent to a third If 1 2, and 2 3, then 1 3 value, then they are ________________ to each other. Remember: Distributive Property!!! _____________________________________________________ Fill in the reason that justifies each step. 1. 0.25x + 2x + 12 = 39 2.25x + 12 = 39 2.25x = 27 225x = 2700 x = 12 Given a. b. c. d. 2. Given: mABC = 80 mABD 3x 3 , mCBD 6 x 5 , mABC = 80 Given mABD + mDBC = mABC Angle Addition Postulate (3x + 3) + (6x + 5) = 80 Substitution Property 9x + 8 = 80 a. 9x = 72 b. x=8 c. A ___________ is an argument that uses deductive reasoning to show why something is true. A _________________ proof is one type of proof. Each statement is on the left, and your justification, or reason, is on the right. A reason may be a ____________, ______________, ______________, or ______________,. A list of properties is on page 841. A list of postulates and theorems starts on page 842. Use these pages as a reference! Ex: Write the reasons for this two-column proof. Given: QWT and TWX are complementary. Prove: x = 28 Statements Reasons 1) QWT and TWX are complementary 1) mQWT 2 x , mXWT x 6 2) mQWT + mTWX = 90 2) 3) 2x + x + 6 = 90 3) 4) 3x + 6 = 90 4) 5) 3x = 84 5) 6) x = 28 6) Ex: Fill in the missing statements or reasons for the two-column proof. Given: E is the midpoint of DF . Prove: DE = 23 Statements 1) E is the midpoint of DF . DE 6 x 4 , EF 8 x 1 2) Reasons 1) 2) Definition of midpoint 3) 6x + 5 = 8x – 1 3) 4) 5 = 2x – 1 4) 5) 5) Addition Property of Equality 6) 6) Division Property of Equality 7) DE = 6(3) + 5 7) 8) DE = 23 8)