This document defines and describes the properties of a kite shape in geometry. It states that a kite has two pairs of consecutive congruent sides, perpendicular diagonals, one pair of opposite congruent angles, one diagonal that forms two isosceles triangles, and one diagonal that bisects the other diagonal. It provides examples of using kite properties to solve for missing side lengths, angles, and finding the area of a kite given the lengths of its diagonals.

1. Kite
A kite is a quadrilateral
with two distinct
pairs of consecutive
sides that are congruent.

2. Properties of Kite
Two pairs of adjacent sides are congruent
F
A
I
R
𝐹𝐴 ≅ 𝐴𝐼
𝐹𝑅 ≅ 𝑅𝐼

3. Lesson 6-5: Trapezoid &
Kites
3
The diagonals of a kite are perpendicular.
𝐴𝑅 ⊥ 𝐹𝐼
F
A
I
R
Properties of Kite
Y

4. Lesson 6-5: Trapezoid &
Kites
4
Properties of Kite
It has one pair of opposite angles that are congruent
∠𝐴𝐹𝑅 ≅ ∠𝐴𝐼𝑅
F
A
I
R
Y

5. Lesson 6-5: Trapezoid &
Kites
5
Properties of Kite
It has one diagonal that forms two isosceles triangles.
∆𝐹𝐴𝐼 𝑎𝑛𝑑 ∆𝐼𝑅𝐹 are isosceles triangles
F
A
I
R

6. Lesson 6-5: Trapezoid &
Kites
6
Properties of Kite
It has one diagonal that forms two congruent triangles.
F
A
I
R
∆𝐴𝐹𝑅 ≅ ∆𝐴𝐼𝑅

7. Lesson 6-5: Trapezoid &
Kites
7
Properties of Kite
It has one diagonal that bisects a pair of opposite
angles.
∠𝐹𝐴𝑅 ≅ ∠𝐼𝐴𝑅
∠𝐹𝑅𝐴 ≅ ∠𝐼𝑅𝐴
F
A
I
R

8. Lesson 6-5: Trapezoid &
Kites
8
Properties of Kite
A kite has one diagonal that bisects the other diagonal.
F
A
I
R
Y
𝐹𝑌 ≅ 𝐼𝑌

9. Lesson 6-5: Trapezoid &
Kites
9
Kite
The area of a kite is half the product of the lengths of
its diagonals.
𝐴𝑟𝑒𝑎 𝑜𝑓 𝐾𝑖𝑡𝑒 =
1
2
𝐴𝑅 𝐹𝐼
F
A
I
R

10. Kite
Given: Kite TASK
T
A
S
K
If TA = 7, then AS = _____.
If m∠𝐴𝑇𝐾 = 118, 𝑡ℎ𝑒𝑛 𝑚 ∠𝐴𝑆𝐾 = ________.
If m∠𝑇𝐴𝐾 = 42, 𝑡ℎ𝑒𝑛 𝑚 ∠𝑇𝐴𝑆 = __________.
If TS = 10, then TY = ________.
If AS = 7 and TK = 11, the perimeter of kite
TASK is________.
7
118
84
5
36
Y

11. Kite
Given: Kite TASK
T Y S
K
If AK = 9 cm and TS = 6 cm, the area
of kite TASK is ________.
𝐴𝑟𝑒𝑎 𝑜𝑓 𝐾𝑖𝑡𝑒 =
1
2
𝐴𝐾 𝑇𝑆
𝐴𝑟𝑒𝑎 𝑜𝑓 𝐾𝑖𝑡𝑒 =
1
2
9 𝑐𝑚 6 𝑐𝑚
𝐴𝑟𝑒𝑎 𝑜𝑓 𝐾𝑖𝑡𝑒 =
1
2
(54𝑐𝑚2)
𝐴𝑟𝑒𝑎 𝑜𝑓 𝐾𝑖𝑡𝑒 =
54𝑐𝑚2
2
𝐴𝑟𝑒𝑎 𝑜𝑓 𝐾𝑖𝑡𝑒 = 𝟐𝟕 𝒄𝒎𝟐
A

12. Activity
Given: Kite CUTE
C
U
T
E
If CU = 15, then UT = _____.
If CT = 26, 𝑡ℎ𝑒𝑛 𝑀𝑇 = ________.
If m∠𝑇𝑈𝐸 = 56, 𝑡ℎ𝑒𝑛 𝑚 ∠𝐶𝑈𝐸 = __________.
If m∠𝑈𝐶𝐸 = 112, then m∠𝑈𝑇𝐸 = ________.
If UE = 12 and CT = 5, find the area of kite.
M