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
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.
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.
4x+9= -3x+2 14x+3(7-x) =-1
Page 108 3-14
Homework: page 111 Quiz 2.4-2.5
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.
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
Angle Addition Postulate
Substitution Property
Substitution Property
In the diagram, m ABD=∠ m CBE. Show that m 1=∠ ∠ m 3.∠A
BC
D
E
12
3
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 109 15, 16, 21-25, 28, 31, 33