Properties+of+Equality

Lena W., Kate W., Hannah T., Rachel T.  Let a,b,c be real numbers...

**Addition Property-** If a=b, then a+c=b+c **Subtraction Property-** If a=b, then a-c=b-c **Multiplication Property**- If a=b, then ac=bc **Division Property-** If a=b and c is not equal to 0, then a/c= b/c **Substitution Property-** If a=b, then a can be substituted for b in any equation or expression **Distributive Property-** a(b+c)= ab+ac, where a,b and c are real numbers

Reflexive Properties- Symmetric Property- Transitive Property-
 * Real Numbers:For any real numbers a, a=a
 * Segment Length: For any segment AB, AB=AB
 * Angle Measure: For any angles <A, m<A=m<A
 * Real Numbers: For any real numbers a and b, if a=b, then b=a
 * Segment Length: For any segments AB and CD, if AB=CD, then CD=AB
 * Angle Measure: For any angles 1) If a=b, b= 16, and c= 12  a+c=c+b  2) If d=e, e=4, and = 44  d+e=e+f   **Subtraction Property**  3) If a=b, b= 12, and c= 6  a-c=b-c  4) If d=e, e=32, and f= 2  e-f=d-f   **Multiplication Property**  5) If a=b, b=4, and c=10  ab=bc  6) If d=e, e=2, and f=8  de=ef  **Division Property ** 7) If a=b, b=2, and c=3  a/c=b/c  8) If d=e, e=12, and f=6  <span style="color: #00ff00; font-family: 'Comic Sans MS',cursive; font-size: 130%;">d/f=e/f  **<span style="color: #800080; font-family: 'Comic Sans MS',cursive; font-size: 160%;">Substitution Property ** <span style="color: #00ff00; font-family: 'Comic Sans MS',cursive; font-size: 130%;">9) If a=b, and a= 8 solve this:  <span style="color: #00ff00; font-family: 'Comic Sans MS',cursive; font-size: 130%;">2b+16  <span style="color: #00ff00; font-family: 'Comic Sans MS',cursive; font-size: 130%;">10) If c=d, and c=13 solve this:  <span style="color: #00ff00; font-family: 'Comic Sans MS',cursive; font-size: 130%;">d+13-10  **<span style="color: #800080; font-family: 'Comic Sans MS',cursive; font-size: 160%;">Distributive Property ** <span style="color: #00ff00; font-family: 'Comic Sans MS',cursive; font-size: 130%;">11) Solve this:  <span style="color: #00ff00; font-family: 'Comic Sans MS',cursive; font-size: 130%;">2(8-1)  <span style="color: #00ff00; font-family: 'Comic Sans MS',cursive; font-size: 130%;">12) Solve this:  <span style="color: #00ff00; font-family: 'Comic Sans MS',cursive; font-size: 130%;">10(15+5)   **<span style="color: #800080; font-family: 'Comic Sans MS',cursive; font-size: 160%;">Identify which property is being shown: ** <span style="color: #00ff00; font-family: 'Comic Sans MS',cursive; font-size: 130%;">13) If <C=<B, then <B=<C  <span style="color: #00ff00; font-family: 'Comic Sans MS',cursive; font-size: 130%;">14) If x+d=22 and d=15, then x+15=22  <span style="color: #00ff00; font-family: 'Comic Sans MS',cursive; font-size: 130%;">15) C=C  <span style="color: #00ff00; font-family: 'Comic Sans MS',cursive; font-size: 130%;">16) AB=BA  <span style="color: #00ff00; font-family: 'Comic Sans MS',cursive; font-size: 130%;">17) If EF=GH and GH=IJ, then EF=IJ  __<span style="color: #800000; font-family: 'Arial Black',Gadget,sans-serif; font-size: 170%;">Answers __ <span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 140%;">1) 28=28 <span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 140%;">2) 48=48 <span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 140%;">3) 6=6 <span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 140%;">4) 30=30 <span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 140%;">5) 40=40 <span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 140%;">6) 16=16 <span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 140%;">7) 2/3=2/3 <span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 140%;">8) 2 <span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 140%;">9) 32 <span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 140%;">10) 16 <span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 140%;">11) 14 <span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 140%;">12) 200 <span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 140%;">13) Symmetric POE <span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 140%;">14) Transitive POE <span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 140%;">15) Reflexive POE <span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 140%;">16) Symmetric POE <span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 140%;">17) Transitive or Substitution POE

<span style="color: #ff00ff; display: block; font-family: 'Comic Sans MS',cursive; font-size: 160%;">Helpful Resources: [|Properties of Equality Website] [|Properties of Equality Website 2] [|Properties of Equality Video] [|Properties of Equality Worksheet] [|Properties of Equality Quiz Yourself]

= PROPERTIES OF EQUALITY =

ADDITION- Kaitlyn F.
If A = B, then A + C = B + C

EX: SOLVE 2X + 5 = 20 - 3X....... IF YOU ADD 3X THEN THAT IS AN EXAMPLE OF THE ADDITION PROPERTY OF EQUALITY

__SUBTRACTION:by Maggie Rellihan__
if A=B, Then A-C=B-C For example: A=3. So, 3-C=B-C.

MULTIPLICATION
= if a=b then ac=bc = = BECAUSE if a and b are equal to each other, then a multiplied by c will be the same as b multiplied by c = = for example: if a = 6, c=2, and a=b then 6(2)=6(2) 12=12=

= ﻿DIVISION- Elena Flo = = what you divide by one side of the equal sign, you have to do the same to the other side of the equal sign. = EXAMPLE: if AB=CB thenAB=CB /B /B ( if u divide AB by 'b', then you have to divide CB by 'b') A= C ( this is the division property of equality) = i.e. 3x=9 = = /3 /3 = = x=3 = = Practice: 12b=36 = = line 2? = = line 3? =

__ ﻿ ﻿ ﻿ SUBSITUTION:Elena FLO__
<span style="background-color: #7924ff; color: #fefd8a; display: block; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 170%;">if a = b, then a can be substituted for b in any expression and vice versa. Example: if a=d, then b=d. a and b can be interchanged throughout equations and problems.

Practice: if the measure of angle ABC= DEF, and the measure of angle DEF =the measure of angle GHI then what does ABC also equal? <span style="background-color: #7924ff; color: #fefd8a; display: block; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 170%;">BY: MEGHAN MAGGIE KAITLYN AND ELENA