Regular polygons constructed on the sides of an arbitrary triangle often lead to intriguing configurations with triples of concurrent lines. We state and prove two general theorems covering many such configurations. The theorems are illustrated by many examples.

Note: This is an Accepted Manuscript of an article published by Taylor & Francis in the American Mathematical Monthly on 30 Jan 2019, available online at ''doi.org/10.1080/...''.

We present several problems that can be solved in a very short way using properties of a glide reflection. In our configurations the glide reflection will be obtained as a composition of three reflections.

Note: This paper is dedicated to the memory of Professor Edmund Puczyłowski.