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Bellwork. .Have your notes ready to go. On an index card create this graphic organizer and be ready to fill it out. ~p ~q. q p. p q. ~q ~p. p q. Chapter 2-5. Reasoning in Algebra & Geometry. Properties of Equality. Properties of Equality. Distributive Property.
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Bellwork .Have your notes ready to go. • On an index card create this graphic organizer and be ready to fill it out.
~p~q qp pq ~q~p pq
Chapter 2-5 Reasoning in Algebra& Geometry
Using The Properties Name the Property that justifies each step. 1) 3x = 18 x = 6 2) 4x – 3 = 13 4x = 16 Division Property of Equality Addition Property of Equality
Using The Properties Name the Property that justifies each step. 1) 5x +3 = 18 5x = 15 2) 2(x – 5) = 9 2x - 10 = 9 Subtraction Property of Equality Distributive Property
Using The Properties Name the Property that justifies each step. 1) Angle A = Angle B Angle B = Angle C Angle A = Angle C 2) 4x= 3x + 3 3x + 3 = 4x Transitive Property Symmetric Property
O (10x +3) (7x +7) M L N Angle LMO + Angle OMN are supplementary Angle LMO + Angle OMN = 180 (7x+7) + (10x + 3) = 180 17x + 10 = 180 17x = 170 x = 10 • linear pairs are supplementary. • 2) Definition of supplementary • 3) Substitution Property • 4) Distributive Property • 5) Subtraction POE • 6) Division POE
Q (5x -12) (5x -8) S R T Angle RSQ + Angle QST are supplementary Angle RSQ + Angle QST = 180 (5x - 8) + (5x - 12) = 180 10x - 20 = 180 10x = 200 x = 20 • linear pairs are supplementary. 2) Definition of Supplementary Angles 3) Substitution Property 4) Distributive Property 5) Addition POE 6) Division POE
(7x + 4) (3x + 6) A B C Given: AC = 30Find: x StatementsReasons 1) AC = 30 1) Given 2) AB + BC = AC 2) Segment Addition Postulate 3) (7x+4) + (3x+6) = 30 3) Substitution Property 4) 10x + 10 = 30 4) Distributive Property 5) 10x = 20 5) Subtraction POE 6) x = 2 6) Division POE
B A (2x - 5) (x + 6) C D Given: line DB bisects angle ADCFind: x StatementsReasons 1) Line DB bisects angle ADC 1) Given 2) Angle ADB = Angle BDC 2) Definition of bisects 3) 2x - 5 = x + 6 3) Substitution Property 4) x – 5 = 6 4) Subtraction POE 5) x = 11 5) Addition POE
Homework: WB pg. 51