These sailboats are participating in a race. To make the race fair, all sailboats must be the same size and shape. Since the sails of each boat have the same size and shape, they are congruent triangles.
Courtesy of Boatsand.boating.com
Image source: http://cpcug.org/user/tobyw/LARC/8_5_01_Roll_3_Mvc-005f_gamma.jpg
Two pairs of congruent angles are found in each set of cross beams.
Image source: http://www.presentersonline.com/resources/clipart/gifs/road_signs.gif
Most polygon shaped road signs have congruent angles.