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Chapter 2 Lesson 4

Chapter 2 Lesson 4. Objective : To connect reasoning in algebra to geometry. Properties of Equality. Addition Property If a=b, then a+c = b+c Subtraction Property If a=b, then a-c = b-c Multiplication Property If a=b, then a•c = b•c

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Chapter 2 Lesson 4

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  1. Chapter 2 Lesson 4 Objective: To connect reasoning in algebra to geometry.

  2. Properties of Equality • Addition Property If a=b, then a+c = b+c • Subtraction Property If a=b, then a-c = b-c • Multiplication Property If a=b, then a•c = b•c • Division Property If a=b and c≠0, then a/c = b/c • Reflexive Property a = a • Symmetric Property If a=b, then b=a • Transitive Property If a=b and b=c, then a=c • Substitution Property If a=b, then b can replace a in any expression

  3. If point B is in the interior of AOC, then m AOB + m BOC = m AOC. • B • O The Distributive Property a(b+c) = ab + ac Angle Addition Postulate • A C

  4. • B • Given: m AOC = 139 A • O C m AOB + m BOC = m AOC Example 1: Solve for x and justify each step. x° (2x + 10)° Angle Addition Postulate x + 2x + 10 = 139 Substitution Property 3x + 10 = 139 Simplify 3x = 129 Subtraction Property of = x = 43 Division Property of =

  5. Example 2: Justify each step used to solve 5x – 12 = 32 + x for x. 5x = 44 + x 4x = 44 X = 11 Addition Property of Equality Subtraction Property of Equality Division Property of Equality

  6. • M • K (2x + 40)° • 4x° LM bisects KLN Given m MLN = m KLM Definition of angle bisector 4x = 2x + 40 _____________________ 2x = 40 _____________________ x = 20 _____________________ L N Example 3: Fill in each missing reason. Substitution Prop. Subtraction Prop. of Equality Division Prop. Of Equality

  7. 2y 3y-9 A B C Example 4: Solve for y and justify each step. Given: AC = 21 AB + BC = AC 2y + (3y – 9) = 21 5y – 9 = 21 5y = 30 Y = 6 Segment Addition Postulate Substitution Property Simplify Addition Property of Equality Division Property of Equality

  8. Properties of Congruence Reflexive Property AB AB A A Symmetric Property If AB CD, then CD AB If A B, then B A Transitive Property If AB CD and CD EF, then AB EF If A B and B C, then A C.

  9. a. K K d. If RS TW and TW PQ, then RS PQ. Example 5: Name the property of equality or congruence that justifies each statement. Reflexive Property of Congruence b. If 2x – 8 = 10, then 2x = 18 Addition Property of Equality c. If x = y and y + 4 = 3x, then x + 4 = 3x. Substitution Property of Equality Transitive Property of Congruence

  10. Homework Page 91-93 #1-30

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