1. Draw a ⊥ segment from C that intersects #&\overleftrightarrow{\sf AB}#& at D.
2. Draw a different segment, #&\overline{\sf CE}#&, to #&\overleftrightarrow{\sf AB}#&.
3. def. of right triangle
4. #&\overline{\sf CE}#& is the hypotenuse of
△ ECD.
5. #&\overline{\sf CE}#& is the longest side of
△, ECD so CD < CE.
6. The shortest dist. from C to #&\overleftrightarrow{\sf AB}#& is CD.
6. conclusion from step 5