1. Properties of Equality and Congruence Section 2.6

2. 2 PROPERTIES OF EQUALITY: ALGEBRAIC REVIEW REFLEXIVE PROPERTY OF EQUALITY: For any real number a, a=a 5=5 -10=-10 SYMMETRIC PROPERTY OF EQUALITY: For all real numbers a and b, if a=b, then b=a X=5 5=X 6X-12=8 8=6X-12 9Y -2Y +1= 3X 2 3X= 9Y -2Y+1 2 STANDARDS 1,2,3 TRANSITIVE PROPERTY OF EQUALITY: For all real numbers a, b, and c, if a=b, and b=c then a=c If X=6 and Y= 6 then X=Y If Y=2X+2 and Y=6-3X then 2X+2=6-3X PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

3. 3 STANDARDS 1,2,3 of segments is transitive. of s is transitive of segments is symmetric. of s is symmetric of segments is reflexive. of s is reflexive KL LM AB KL AB KL LM KL LM BCE FGH ECA BCE ECA BCE FGH BCE FGH ECA Congruence in segments and angles is Reflexive, Symmetric and Transitive: For all segments and angles, their measures comply with these same properties. PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

4. 4 ADDITION AND SUBTRACTION PROPERTIES OF EQUALITY: PROPERTIES OF EQUALITY: ALGEBRAIC REVIEW For any numbers a, b, and c, if a=b then a+c=b+c and a-c=b-c 10 = 10 + 6 +6 16 = 16 22 = 22 -5 17 = 17 STANDARDS 1,2,3 SUBSTITUTION PROPERTY OF EQUALITY: If a=b, then a may be replaced by b. b=2 and3b +1=7 If then 3( )+1=7 2 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

5. 5 MULTIPLICATION AND DIVISION PROPERTIES OF EQUALITY: PROPERTIES OF EQUALITY For any real numbers a, b, and c, if a=b, then a c=b c and if c=0, = a c b c 15 = 15 2 2 30 = 30 28 = 28 7 4 = 4 24 = 24 3 3 72 = 72 36 = 36 12 3 = 3 STANDARDS 1,2,3 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved