Section 2.5. Addition PropertyIf a=b, then a+c=b+c If 2=2, then 2+1=2+1 Subtraction PropertyIf a=b, then a-c=b-c If 2=2, then 2-1=2-1 Multiplication PropertyIf.

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Presentation transcript:

Section 2.5

Addition PropertyIf a=b, then a+c=b+c If 2=2, then 2+1=2+1 Subtraction PropertyIf a=b, then a-c=b-c If 2=2, then 2-1=2-1 Multiplication PropertyIf a=b, then ac=bc If 2=2, then 2(3)= 2(3) Division PropertyIf a=b and c≠0, then a/c=b/c If 2=2, then 2/4=2/4 Substitution PropertyIf a=b, then a can be substituted for b in any equation. Distributive PropertyIf a, b and c are real numbers, then a(b+c)= ab+ac If a=2, b=3 and c=x, then 2(3+x)= 6+2x

 6x+2= -3x-16  +3x +3x  9x+2= -16   9x= -18  X=- 2  Given  Addition Property  Subtraction Property  Division Property Solve 6x+2= -3x-16 for x. Write your reason for each step.

 3x+8= -4x-34  +4x +4x  7x+8= -34   7x= -42  x= -6  Given  Addition Property  Subtraction Property  Division Property Solve 3x+8= -4x-34 for x. Write your reason for each step.

 4x+9= -3x+2  14x+3(7-x) =-1

 Page  Homework: page 111 Quiz

Reflexive PropertyFor real numbers, a=a. 2=2 For segment lengths, AB=AB. For any angle A, m ∠ A= m ∠ A Symmetric PropertyFor any real numbers a and b, if a=b then b=a. For segment lengths, if AB=CD then CD=AB For any angle, if m ∠ A=m ∠ B then m ∠ B=m ∠ A Transitive PropertyFor any real numbers a, b and c, if a=b and b=c, then a=c For segment lengths, if AB=CD and CD=EF, then AB=EF. For any angle, if m ∠ A=m ∠ B and m ∠ B=m ∠ C, then m ∠ A=m ∠ C.

 m ∠ ABD=m ∠ CBE  m ∠ ABD-m ∠ 2= m ∠ 1  m ∠ CBE-m ∠ 2= m ∠ 3  m ∠ ABD-m ∠ 2= m ∠ CBE-m ∠ 2  m ∠ 1= m ∠ 3  Given  Angle Addition Postulate  Substitution Property In the diagram, m ∠ ABD=m ∠ CBE. Show that m ∠ 1=m ∠ 3. A B C D E What do we know? What’s given to us? What do I need to do to get angle 1? What about angle 3? How are these angles related? How do I know they are equal?

 If m ∠ 6= m ∠ 7, then m ∠ 7=m ∠ 6.  Symmetric Property  If JK=KL and KL=MN, then JK=MN.  Transitive Property  m ∠ 6=m ∠ 6.  Reflexive Property  If m ∠ A=m ∠ B and m ∠ B=m ∠ C, then m ∠ A=m ∠ C.  Transitive Property  If XY=WZ, then WZ=XY.  Symmetric Property  AB=AB  Reflexive Property

 Complete in your notebooks.  Page , 16, 21-25, 28, 31, 33