Kite
A kite is a geometric figure where each of two adjacent sides are the
same length. Look at the figure below. Notice that the line segment EB is the
same length as CB, and the line segment ED is the same length as CD. Try
clicking on each point and dragging it to see what it does to the figure
(Point E can not be dragged).
 

A kite is a geometric figure where each of two adjacent sides are the same length. Look at the figure below. Notice that the line segment EB is the same length as CB, and the line segment ED is the same length as CD. Try clicking on each point and dragging it to see what it does to the figure (Point E can not be dragged). Look at triangles EBA and CBA. What conjecture can you make about these triangles? Now look at triangles EDA and CDA. What conjecture can you make about these triangles? How could you prove such a conjecture?
A kite is a geometric figure where each of two adjacent sides are the same length. Look at the figure below. Notice that the line segment EB is the same length as CB, and the line segment ED is the same length as CD. Try clicking on each point and dragging it to see what it does to the figure (Point E can not be dragged). Look at triangles EBA and CBA. What conjecture can you make about these triangles? Now look at triangles EDA and CDA. What conjecture can you make about these triangles? How could you prove such a conjecture? Note that triangles EBC and EDC are isosceles triangles. What do we know about isosceles triangles that might help you?
Now look at line segment EC. Is the conjecture that A is the bisector of line segment EC reasonable? How might you use a proof that triangle EBA is congruent with triangle CBA to prove that A is the bisector of EC?
The circle that circumscribes triangle BED has been drawn. Manipulate the kite by dragging point O (the center of the circle) until point C is on the circle. What can you conjecture about a kite that can be inscribed in a circle? How could you prove such a conjecture?

