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Quadrilateral Angle Bisector Problem

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Description:

Source(s):
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

Other Variants: See Keyton (1997) for properties that suggest new problems




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Prior knowledge 

Prior DGS content required:

Angle bisector

Prior mathematical content required:

Quadrilaterals

Prior mathematical content related:

Angle bisectors

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Possible learning

Likely mathematical content learned:

Conditions for a quadrilateral to have an incircle.
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Supported by a research grant from the Social Sciences and Humanities Research Council of Canada

Page last updated July 2008 by David Reid

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