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Warm-Up • How do you balance your life? Section 2.5 (10/07/2013) Learning Target • I am learning the properties of algebra and geometry. a = weighted blocks a a Reflexive Property (Copy this) • Let “a” be a real number. • The property states that: •a = a • Example: •5 = 5 Since the What would blocks happen are the to the same scale weight if I were to start to switch out with, the no blocks to different sides? would change. weight a a = weighted blocks b b = weighted blocks Symmetric Properties (copy this down) • Let “a” and “b” be any real number. • The property say: • If a = b, then b = a. • Example: • 5x + 10 = 20 • 20 = 5x + 10 What would happen if I were to add an “c” block to the left hand side? a c b c = weighted blocks b = weighted blocks a = weighted blocks Now, without removing any blocks. What can you do to The scale would tip downward on the left hand side. You can add “c” block to the right hand side. make the scale balance? a c b c b a c Addition (copy this down) • Let a, b, and c be any real number. • If a = b, then a + c = b + c • Example: • 2x = 10 • 2x + 5 = 10 + 5 What would happen to the scale weight if I replace “a” Nothing, since “b” block is equal withtwo “a”of block. block with two “b” block? b b b a b a b a Substitution Property (copy this) • Let a, b, and c be any real number. • The property states: • If a = b, then b can replace a in any expression • Example: • Let a = b and 5a = 10 • Then we can say 5a = 5b = 10 What would happen if I take 2 “b” blocks away from the right hand side? b b b a b b You can take away 2downward “b” blocks left Without The scale adding would anytipblocks, how would onon thethe you left balance handhand side side. the since scale? it’s heavier. a b b b b a Subtraction Property (copy this) • Let a, b, and c be real numbers. • The property states that: • If a = b, then a – c = b – c. • Example: • 5x = 20 • 5x – 10 = 20 - 10 Let the weight of block “b” Let the weight of block “b” Using the substitution property, we didn’t do and the weight block if replace and“b” the weight of block “c” What wouldofhappen block with anything to change the weight. “a” be equal. be equal. an “a” block? b a c a Transitive Property • Let a, b, and c be real numbers. • The property states: • If a = b and b = c, then a = c • Example: • Let 3x = 5 and let 5 = 2y. • Then 3x = 2y What would happen if I make the left hand side 3 times as heavy? b b b b a It would tilt downward on the left hand side because it’s heavier. a b b b b To balance out the scales, you multiply the weight on the right hand side by 3. b b b b a a a a Multiplication Property (copy this down) • Let a, b, and c be real number. • The property states that: • If a = b, then a ∙ c = b ∙ c. • Example: • 5x + 2 = 10 • 4 5x + 2 = 4 ∙ 10 What would happen I divide the weight on the left hand side in half?? b b b b a a a a Without adding blockstilt ondownward the left handon side, what canhand I do toside It would the right balance outbecause the scale?it’s heavier. b b a a a a To balance out the scale, divide the weight on the right hand side in half. b b a a Division Property • Let “a” and “b” be real numbers. • The property states: 𝑎 𝑐 • If a = b and c ≠ 0, then = • Example: • 3𝑥 − 5 = 10 • 3𝑥−5 2 = 10 2 𝑏 . 𝑐 What is the area??? 4 3 3 ∗ 4 = 12 6 3 ∗ 6 = 18 𝐴 = 3 ∗ 10 = 3 4 + 6 =3∗4+3∗6 Distributive Property • Let a, b, and c be any real numbers. • The property states: • 𝑎 𝑏 + 𝑐 = 𝑎𝑏 + 𝑎𝑐 • Example: • 5(2 + 4) = 5(2) + 5(4) a b c 𝑎∗𝑏 𝑎∗𝑐 Properties of Congruence Reflexive Property: 1) Symmetric Property: 2) Transitive Property: 3) Example: At each step, indicate the properties (congruence or algebraic) that was use. 1) 2) 3) 4) 5) Recap • Properties of Equality (a.k.a. Algebraic Reasoning) • • • • • • • • Additional Subtraction Multiplication Division Reflexive Transitive Symmetric Substitution • Properties of Congruence (a.k.a. Geometric reasoning) • Reflexive • Symmetric • Transitive Reflection • In your own words, what were the learning targets? • On a scale from 1-5 • 1 for not understanding the learning target at all. • 5 for completely understanding the learning target. • Explain