Classwork #4.1 – Properties of Kites
Date ______________
Quadrilateral: ______________________________________________________
____________________________________________________________________
Definition of a Kite: ______________________________________________________
____________________________________________________________________
Parts of a Kite:
Vertex Angles:
Non-vertex angles:
Diagonals:
What properties do you think all Kites have?
Investigation: We are going to look at the sides, angles and diagonals of a Kite and see what
properties we can discover (and prove).
Tools – You can use patty paper, notebook paper, drawings, the definition of a Kite and
relevant properties of triangles to help you.
Your Job: Investigate the following items to see if you can find any relationships that apply to
any arbitrary Kite:
i) Properties of pairs of angles
ii) Relationships between the Diagonals of the Kite
iii) Relationship between the Vertex angles and the Diagonal between them
Suggestions:
1. Play around with the drawing or with patty paper. Look for triangles (maybe add some
auxillary lines). What things turn out to be congruent (anything?) or otherwise related?
2. Organize your ideas into a proof or construct counter-examples that show how these
properties do not always apply.
Four Kite Conjectures
Kite Angles Conjecture: The _______________________ angles of a kite are ________________________. Kite Diagonals Conjecture: The diagonals of a kite are _____________________________. Kite Diagonal Bisector Conjecture: The diagonal connecting the vertex angles of a kite is the ______________________ of the other diagonal. Kite Angle Bisector Conjecture: The __________________ angles of a kite are ___________________ by a ____________________. Problems:
1) Solve for angles x and y in the diagram.
2) If AC = 20 cm, then how long are BC and CD?
BC = _________
CD = _________