section 2.5. addition propertyif a=b, then a+c=b+c if 2=2, then 2+1=2+1 subtraction propertyif a=b,...

Section 2.5

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Section 2.5

Addition Property If a=b, then a+c=b+cIf 2=2, then 2+1=2+1

Subtraction Property If a=b, then a-c=b-cIf 2=2, then 2-1=2-1

Multiplication Property If a=b, then ac=bcIf 2=2, then 2(3)= 2(3)

Division Property If a=b and c≠0, then a/c=b/cIf 2=2, then 2/4=2/4

Substitution Property If a=b, then a can be substituted for b in any equation.

Distributive Property If a, b and c are real numbers, then a(b+c)= ab+acIf a=2, b=3 and c=x, then 2(3+x)= 6+2x

Page 3: 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

6x+2= -3x-16 +3x +3x 9x+2= -16 -2 -2 9x= -18 X=- 2

Given

Addition Property

Subtraction Property

Division Property

Solve 6x+2= -3x-16 for x. Write your reason for each step.

Page 4: 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

3x+8= -4x-34 +4x +4x 7x+8= -34 -8 -8 7x= -42 x= -6

Given

Addition Property

Subtraction Property Division Property

Solve 3x+8= -4x-34 for x. Write your reason for each step.

Page 5: 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

4x+9= -3x+2 14x+3(7-x) =-1

Page 6: 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

Page 108 3-14

Homework: page 111 Quiz 2.4-2.5

Page 7: 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

Reflexive Property For real numbers, a=a. 2=2For segment lengths, AB=AB.For any angle A, m∠A= m∠A

Symmetric Property For any real numbers a and b, if a=b then b=a. For segment lengths, if AB=CD then CD=ABFor any angle, if m∠A=m∠B then m∠B=m∠A

Transitive Property For any real numbers a, b and c, if a=b and b=c, then a=cFor 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.

Page 8: 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

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

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?

Page 9: 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

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

Page 10: 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

Complete in your notebooks. Page 109 15, 16, 21-25, 28, 31, 33

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