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Painless Properties Justify Me 100 100 100 100 100 200 200 200 200 200 300 300 300 300 300 400 400 400 400 400 500 500 500 500 500 Theorem Just the Schmeorem Facts, Ma’am Next in Line If 5x = 25, then x = 5. Division Property mABC = mABC Reflexive Property If 6 = y, then y = 6. Symmetric Property If AB + BC = AC and BC = 10, then AB + 10 = AC Substitution Property If M N, and N Q, then M Q Transitive Property of Congruence Given: C is the midpoint of AB Statement: ACCB Reason: ? Definition of a Midpoint Given: W Y Statement: mW = mY Reason: ? Definition of Congruent Angles Given: ABCD Statement: ABD is a right angle Reason: ? Definition of Perpendicular Lines Given: ABD is a right angle Statement: mABD = 90 Reason: ? Definition of a Right Angle Given: G is a complement of H and J is a complement of H Statement: G J Reason: ? Congruent Complements Theorem 1 2 1 2 Name the theorem. Vertical Angle Theorem A B C AB + BC = AC Name the postulate or theorem. Segment Addition Postulate 1 & 2 are right angles. 1 2 Name the postulate or theorem. Right Angle Congruence 3 & 4 are supplementary. m 3 + m4 = 180 Name the postulate, theorem, or definition. Definition of Supplementary Angles BD bisects ABC. ABD DBC uuuuuuuuuuuuur Name the postulate, theorem, or definition. Definition of an Angle Bisector (1) All cats have fur. (2) Garfield is a cat. (3) ??? Garfield has fur. (1) If it’s Friday, then we don’t have school the next day. (2) We don’t have school tomorrow. (3) It’s Friday. Which Law, if any??? Invalid (1) If a polygon is a triangle, then it has 3 sides. (2) If a polygon has 3 sides, then the sum of the interior angles is 180. (3) Conclusion: ??? If a polygon is a triangle, then the sum of the interior angles is 180. Mrs. D. went to the A & P the last 3 Sundays. Mrs. D. will go to the A & P this Sunday morning. Inductive or Deductive? Inductive Reasoning (1) If you are 18, you can register to vote. (2) Freddy is 18 today. (3) Freddy can register to vote. Which Law, if any??? Law of Detachment Determine the next 2 terms: 3, -6, 12, -24, 48, … -96, 192 1, 1, 2, 3, 5, 8, 13, … is an example of what type of sequence? Fibonacci Determine the next item: Determine the next 2 terms: 1, 1/3, 1/9, 1/27, … 1/81, 1/243 1, 4, 9, 16, 25, 36, … Describe the sequence. Perfect Squares