CLASS INVESTIGATIONS: FRIDAY 10/01

Work in groups: One person should be recorder. There are proofs for the recorder to write up and turn via email.

The sign = will be used to mean congruence when it (hopefully) will not lead to confusion.

Kites

Construct

A kite is a quadrilateral ABDC with AB = AD and CB = CD.

• With your compass, draw a couple of intersecting circles, label some points and draw a kite from this picture.
• Use paper folding and your scissors to cut out a kite.

Investigate, Experiment, Conjecture

The diagonals of the kite are AC and BD.

• Discover and list as many relationships as you can among the angles, sides and diagonals of a (general) kite. State the relationships in as strong a form as you can, using geometrical terminology.

Proofs: written assignment

• Then write down your observations then give proofs of the strongest relationships that you can.

IMPORTANT: You are free to use what we have already proved about isosceles triangles. Also if one proves one fact about kites, you can use that to prove a second property. Just avoid circular logic.

Turn in via email by midnight Monday

The Recorder for the group should write up the proofs as a text file or a Word document or a Sketchpad document and submit the document via email. This means one document per group. All the members of the group should be involved in the editing so that all are responsible for the contents.

THE NAMES OF ALL THE MEMBERS OF THE GROUP SHOULD APPEAR AT THE TOP OF THE DOCUMENT so proper credit can be given.

Send the email to king@math.washington.edu