proving angle relationships

[smart_pirate]

Given: line AB is perpendicular to line BC; <1 and <3 are complementry
Prove: <2 is congruent to <3

Here is the picture to help:

http://img376.imageshack.us/my.php?image=geometryro3.jpg

can anyone please help me with this two colum proof?

 

[soroban]

Hello, smart_pirate!

$\displaystyle \text{Given: line }AB \perp BC;\;\;\angle 1\text{ and }\angle 3\text{ are complementry.}$

$\displaystyle \text{Prove: }\;\angle2 \:=\:\angle 3$

      A
      *         E
      *       *
      *     *
      * 1 *
      * * 2
    B *  *  *  *  * C
         *  3
            *
               *
                  D

$\displaystyle \angle ABC = 90^o\quad\Rightarrow\quad \angle 1 + \angle2 \:=\:90^o \quad\Rightarrow\quad \angle 2 \:=\:90^o - \angle 1$ .[1]

$\displaystyle \angle 1\text{ and }\angle3\text{ are complementary: }\angle 1 + \angle 3 \:=\:90^o \quad\Rightarrow\quad \angle 3 \:=\:90^o - \angle 1$ .[2]

Equate [1] and [2]: . $\displaystyle \angle 2 \:=\:\angle 3$

 

[smart_pirate]

cool thank you!