6.7. Kites http://www.ck12.org
TABLE6.9:(continued)
Statement Reason
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.
Example A
Find the other two angle measures in the kite below.
The two angles left are the non-vertex angles, which are congruent.
130 ◦+ 60 ◦+x+x= 360 ◦
2 x= 170 ◦
x= 85 ◦ Both angles are 85◦.Example B
Use the Pythagorean Theorem to find the length of the sides of the kite.
Recall that the Pythagorean Theorem isa^2 +b^2 =c^2 , wherecis the hypotenuse. In this kite, the sides are all
hypotenuses.
62 + 52 =h^2122 + 52 =j^2
36 + 25 =h^2144 + 25 =j^2
61 =h^2169 =j^2
√
61 =h 13 =jExample C
Find the other two angle measures in the kite below.
The other non-vertex angle is also 94◦. To find the fourth angle, subtract the other three angles from 360◦.
90 ◦+ 94 ◦+ 94 ◦+x= 360 ◦
x= 82 ◦