proving angle relationships

Hello, smart_pirate!

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

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

Code: 
      A
      *         E
      *       *
      *     *
      * 1 *
      * * 2
    B *  *  *  *  * C
         *  3
            *
               *
                  D
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\(\displaystyle \angle ABC = 90^o\quad\Rightarrow\quad \angle 1 + \angle2 \:=\:90^o \quad\Rightarrow\quad \angle 2 \:=\:90^o - \angle 1\) .[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]: . \(\displaystyle \angle 2 \:=\:\angle 3\)

 
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