|Let ABCD be a
quadrilateral. consider the bisectors of its internal angles and the
intersection points H, K, L, M of pairs of consecutive bisectors.
1. Drag ABCD, considering different configurations. What happens the quadrilateral HKLM. What kind of figure does it become?
2. Can HKLM become any quadrilateral? Why?
3. Can HKLM become a point? Which hypothesis about ABCD do you need in order to have this situation?
Write down your conjectures and prove them.
Olivero 2002 p. 262-263
Supported by a research grant from the Social Sciences and Humanities Research Council of Canada
Page last updated July 2008 by David Reid