Objective: To connect reasoning in algebra to geometry.

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Presentation transcript:

Objective: To connect reasoning in algebra to geometry. 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 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

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

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

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

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

Example 4: Solve for y and justify each step. 2y 3y-9 A B C 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

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.

Example 5: Name the property of equality or congruence that justifies each statement. a. K K 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 d. If RS TW and TW PQ, then RS PQ. Transitive Property of Congruence

Homework Page 91-93 #1-30