Download Reason Using Properties from Algebra

Section 2.5
REASON USING PROPERTIES
FROM ALGEBRA
ALGEBRAIC PROPERTIES
Addition Property
If a=b, then a+c=b+c
If 2=2, then 2+1=2+1
Subtraction Property
If a=b, then a-c=b-c
If 2=2, then 2-1=2-1
Multiplication Property If a=b, then ac=bc
If 2=2, then 2(3)= 2(3)
ALGEBRAIC PROPERTIES
Division Property
If a=b and c≠0, then
a/c=b/c
If 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+ac
If a=2, b=3 and c=x, then
2(3+x)= 6+2x
SOLVING EQUATIONS FOR X
Solve 6x+2= -3x-16 for x. Write your reason for
each step.
STATEMENTS
1. 6x+2= -3x-16
+3x
+3x
2. 9x+2= -16
-2 -2
3. 9x= -18
4. X=- 2
REASONS
1. Given
2. Addition Property
3. Subtraction Property
4. Division Property
TRY IN YOUR NOTEBOOKS
Solve 3x+8= -4x-34 for x. Write your reason
for each step.
STATEMENTS
REASONS
1. 3x+8= -4x-34
+4x
+4x
2. 7x+8= -34
-8 -8
3. 7x= -42
1. Given
4. x= -6
4. Division Property
2. Addition Property
3. Subtraction Property
SOLVE THE EQUATION FOR X. WRITE YOUR
REASON FOR EACH STEP: 4X+9= -3X+2
PROPERTIES OF EQUALITY
Reflexive Property
For real numbers, a=a. 2=2
For 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=AB
For 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=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.
HOW DO WE WRITE A PROOF?
In the diagram, m∠ABD=m∠CBE. Show that m∠1=m∠3.
A
1
B
2
3
C
D
E
1. m∠ABD=m∠CBE
1. Given
2. m∠ABD-m∠2= m∠1
2. Angle Addition Postulate
3. m∠CBE-m∠2= m∠3
3. Angle Addition Postulate
4. m∠ABD-m∠2= m∠CBE-m∠2
4. Substitution Property
5. m∠1= m∠3
5. Substitution Property
DETERMINE WHETHER TO USE THE SYMMETRIC PROPERTY,
REFLEXIVE PROPERTY OR TRANSITIVE PROPERTY
1. If m∠6= m∠7, then
m∠7=m∠6.
Symmetric Property
4. If m ∠A=m ∠B and m
∠B=m ∠C, then m ∠A=m
∠C.
Transitive Property
2. If JK=KL and KL=MN,
then JK=MN.
5. If XY=WZ, then WZ=XY.
Transitive Property
Symmetric Property
3. m∠6=m∠6
Reflexive Property
6. AB=AB
Reflexive Property