6.7. Kites http://www.ck12.org
From the definition, a kite is the only quadrilateral that we have discussed that could be concave, as with the case of
the last kite. If a kite is concave, it is called adart. The angles between the congruent sides are calledvertex angles.
The other angles are callednon-vertex angles. If we draw the diagonal through the vertex angles, we would have
two congruent triangles.
Theorem:The non-vertex angles of a kite are congruent.
Proof:
Given:KIT EwithKE∼=T EandKI∼=T I
Prove:^6 K∼=^6 T
TABLE6.9:
Statement Reason
1.KE∼=T EandKI∼=T I Given
2.EI∼=EI Reflexive PoC- 4 EKI∼= 4 ET I SSS
4.^6 K∼=^6 T CPCTC
Theorem:The diagonal through the vertex angles is the angle bisector for both angles.
The proof of this theorem is very similar to the proof above for the first theorem. If we draw in the other diagonal in
KIT Ewe find that the two diagonals are perpendicular.
Kite Diagonals Theorem:The diagonals of a kite are perpendicular.
To prove that the diagonals are perpendicular, look at 4 KET and 4 KIT. Both of these triangles are isosceles
triangles, which meansEIis the perpendicular bisector ofKT(the Isosceles Triangle Theorem). Use this information
to help you prove the diagonals are perpendicular in the practice questions.