Algebraic Properties of Equality (POE)
***POE­Property of Equality
Distributive Property
Let a, b, and c be real number:
ADDITION POE
If a=b, then a + c=b + c
SUBTRACTION POE
If a=b, then a­c=b­c
MULTIPLICATION POE
If a=b, then ac=bc
DIVISION POE
If a=b and , then SUBSTITUTION POE
If a=b, then a can be substituted for b in any equation or expression. where a, b, and c are real numbers.
Example of how to use this properties when solving:
Solve for Given
Distributive
Subtraction POE
Addition POE
Division POE
Sep 8­9:39 PM
Write a reason for each step.
­4(11x + 2) = 80
Oct 1­7:20 PM
Try on your own!
­4(11x + 2) = 80
Oct 1­7:40 PM
Sep 27­9:34 AM
Other Properties of Equality
Congruence of Segments
REFLEXIVE
REFLEXIVE
SYMMETRIC
SYMMETRIC
TRANSITIVE
TRANSITIVE
Oct 1­7:25 PM
Oct 1­7:25 PM
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Proof
A proof is a logical argument that shows a statement is true. (ie. Law and Order).
Congruence of Angles
REFLEXIVE
SYMMETRIC
TRANSITIVE
Oct 1­7:25 PM
Sep 30­1:54 PM
Completing Statements
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(Partner Activity)
?
Substitution POE: If AB = 20, then AB + CD = 20 + CD
AB = CD, Show that AC = BD
A
B
C
D
Symmetric POE: If the measure of angle 1 = the measure of angle 2, then
?
?
CD
AB
Addition POE: If AB = CD, then + EF = + EF.
AB = CD
?
?
Given
Distributive POE: If 5(x + 8) = 2, then x + = 2.
40
5
AC = AB + BC
Segment Add. Pos
BD = BC + CD
Segment Add. Pos
Transitive POE: If measure of angle 1 = measure of angle 2, and the measure of angle 2 = measure of angle 3, then ?
AB + BC = CD + BC
Addition POE
Error Analysis (Find the error!)
AC = BD
Substitution Prop
7x = x + 24 Given
8x = 24 Addition POE
Division POE
x = 3
Added x, should of subtracted x
?
Sep 24­12:18 PM
Sep 27­8:21 AM
Homework:
Workbook pages 34&35
Sep 27­8:49 AM
Sep 27­8:49 AM
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