GEOMETRY
Proportion Properties
NAME_________________________
DATE __________ Per.___________
Similarity
1.
A)
B)
C)
D)
E)
Supply the missing Reasons to prove the
Means-Extremes Property of Proportions.
a c
=
b d
a
c
(bd ) = (bd )
b
d
 b
 d
ad   = bc  
 b
 d
ad ⋅ 1 = bc ⋅1
ad = bc
What is the more common
name of this property?
3.
Supply the missing steps to prove the ExtremesExchange Property of Proportions.
A)
GIVEN
B)
Multiplication Property of Equality
C)
Commutative Property of Multiplication
D)
Inverse Property of Multiplication
E)
Multiplicative Identity Property
5.
A)
B)
C)
D)
7.
Justify each step with a property of equality.
Why might this be called the “Add 1” property?
a c
=
b d
a
c
+ 1 = +1
b
d
a b c d
+ = +
b b d d
a+b
=
Distributive Property
b
Fill in the missing Steps to prove the MeansSwitch Property of Proportions.
a
=
A)
GIVEN
b
a  b
B)   =   Multiplication Property of Equality
  d c
2.
C)
=
D)
a
(1) =
c
E)
=
4.
b  c  Commutative Property of Multiplication
 
d c
Multiplicative Inverse Property
Use the Properties of Proportions to prove the
Reciprocal Property of Proportions.
A)
a c
=
b d
B)
=
C)
d b
=
c a
D)
=
6.
a+c
=
b+d
c+e
=
d+ f
a+c+e
=
b+d + f
b) Do you think the following
property is true?
a c e
= = = L, then
b d
f
a+ c+ e+L a c e
= = = = L.
b + d + f +L b d
f
If
_______________________
Means-Switch Property
_______________________
Symmetric Property of Equality
Is there a “Subract 1” property? If so, prove it.
If not, find a numerical counterexample.
a) Find each ratio when a = 2, b = 4, c = 3, d = 6, e = 5, f = 10.
a
=
b
c
=
d
e
=
f
Identity Property of Multiplication
c) Can you prove or disprove this
“infinite addition” property?