Transcript 2-4 Reasoning in Algebra - Village Christian Schools

2-4
Reasoning in Algebra
(7 cards)
Addition/Subtraction Property
 Add or subtract the same number
from both sides of an equation
4 + x = 12
-4
-4
X=8
(Subtraction Property)
Multiplication/Division Property
 Multiply or divide the same number
on each side of an equation
8x = 56
8
8
X=7
(Division Property)
Reflexive Property
 A number, segment or angle is equal
or congruent to itself
5=5
c=c
AB  AB
A  A
Symmetric Property
 Two equal numbers, segments or
angles are equal or congruent to its
converse
If a = b, then b = a
If AB  CD then CD  AB
If A  B then B  A
Transitive Property
 The law of syllogism applied to
numbers, segments and angles
If a = b and b = c, then a = c
If AB  CD and CD  EF, then AB  EF
If A  B and B  C, then A  C
Substitution Property
 Equivalent numbers, segments and
angles can replace each other
If a = b then a can repalce b in any
expression or equation
If AB  CD then AB can replace CD in
any expression or equation
If A  B then A can replace B in
any expresion or equation
Distributive Property
 a(b + c) = ab + ac
Ex 1
Justify each step to solve for x
given mAOC = 139
B
x
A
O
(2x + 10)
C
Ex 1
Justify each step to solve for x
mAOC = 139
Given
B
x
A
O
(2x + 10)
C
Ex 1
Justify each step to solve for x
mAOC = 139
Given
mAOB + mBOC = mAOC Angle Addition Postulate
B
x
A
O
(2x + 10)
C
Ex 1
Justify each step to solve for x
mAOC = 139
Given
mAOB + mBOC = mAOC Angle Addition Postulate
x + 2x + 10 = 139
Substitution
B
x
A
O
(2x + 10)
C
Ex 1
Justify each step to solve for x
mAOC = 139
Given
mAOB + mBOC = mAOC Angle Addition Postulate
x + 2x + 10 = 139
3x + 10 = 139
Substitution
Simplify
Ex 1
Justify each step to solve for x
mAOC = 139
Given
mAOB + mBOC = mAOC Angle Addition Postulate
x + 2x + 10 = 139
3x + 10 = 139
3x
-10
-10
= 129
Substitution
Simplify
Subtraction Property
Ex 1
Justify each step to solve for x
mAOC = 139
Given
mAOB + mBOC = mAOC Angle Addition Postulate
x + 2x + 10 = 139
3x + 10 = 139
3x
3
-10
-10
= 129
Substitution
Simplify
Subtraction Property
3
x = 43
Division Property
Ex 2
Justify each step to solve for x
 Suppose points A, B and C are
collinear with point B between points
A and C. Solve for x if AB = 4 + 2x,
BC = 15-x and AC = 21
Ex 3
Justify each step to solve for x
 Given ray LM bisects angle KLN. The
measure of angle KLM is 2x+40 and
the measure of angle MLN is 4x.
Homework