- The statementis true in the caseof an equilateraltriangle.In addition,for squaresthe statementis also
true. - We do not get six congruenttrianglesas before.But we get four congruenttrianglesand a separatepair
of congruenttriangles.In addition,if we connectthe pointswherethe bisectorsintersectthe sides,we get
an isoscelestriangle. - Fromour previousexerciseswe saw that we couldinscribeand circumscribesomebut not all typesof
quadrilaterals.Drawingfrom thoseexercises,we see that we couldcircumscribeand inscribea square.So,
locatingthe pointsat and is one suchpossibility. Similarly, we couldlocatethe pointsat
and and get a kite that can be inscribedbut not circumscribed.- The fold line dividesthe triangleinto two congruenttrianglesand thus is a line of symmetryfor the triangle.
Notethat the samepropertywill hold by foldingat eachof the remainingangles.