Geometry Test Help Please?!

Here's a few

First one :

AC / BC  = DF  = EF

12 / 18   =  10 / EF

2 / 3   =  10   /  EF      and we can write

3/2  =  EF / 10           multiply both sides by 10

10 (3/2)  = EF  =  15

Second one :

SSS  Similarity Theorem

Third one  :

x / 42  =  6  /36

x / 42   =  1 / 6

6x  =  42

x  =  7 cm

Fourth one :

Proportional

c²

Segment Addition Postulate

Fifth one....1st part

Corresponding Angles Postulate

2nd part

 ΔACE   similar to  Δ BCD

Segment Addition Postulate

Sixth one  :

Definition of Angle Bisector

Angle ADB  congruent to  Angle CDF

Substitution Property

Seventh One :

DB  / BA   =  CE  / AC

6  /  15  =  CE  /  25

2 / 5   =  CE  / 25     multiply through by 25

(2 / 5) (25)  =  CE   =  10

Eighth one :

CB  / CA    =  BD   / AD

7.5 / 4   =  BD   / 3        mutiply through by 3

(3/4) (7.5)   =  BD   =  x  =    5.625

Ninth one :

Definition of Bisector

Alternate Interior Angles Theorem

Substitution Property

Tenth one  :

[ x + 8 ]  / 10  =  [2x + 5 ] / 14      cross-multiply

14 [ x + 8 ]  =  10  [ 2x - 5 ]

14x + 112  =  20x - 50         add 50 to both sides, subtract 14x from both sides

162  =  6x              divide both sides by 6

27  =  x   

Last one :

Base  =  √ [ 18^2   - 9^2 ]   =  9√ [ 2^2 - 1^2 ]  =  9√3   ≈ 15.6 in