Grade 9 Mathematics

1. GRADE QUARTER III
MATHEMATICS

2. Lesson Objective:
a) determine properties of a kite.
b) use properties to find the measure of sides, angles and
other quantities involving kites.
c) solve problems involving kite.
d) appreciate the value of kite to real-life situations

3. KITE
- is a quadrilateral with
two distinct pairs of
consecutive sides that are
congruent.
-the congruent sides
are consecutive.
𝐴𝐵 ≅ 𝐵𝐶 , 𝐶𝐷 ≅ 𝐴𝐷

4. PROPERTIES OF KITE
1. Diagonals are
perpendicular.
 𝐵𝐷 ⊥ 𝐶𝐴

5. PROPERTIES OF KITE
2. Exactly one pair of
opposite congruent angles .
 𝑚∠𝐴 = 𝑚∠𝐶

6. PROPERTIES OF KITE
3.Only one diagonal that bisects the
other diagonal
 Diagonal 𝐾𝑇 bisects diagonal 𝐼𝐸. 𝑇ℎ
𝑖𝑠 𝑚𝑒𝑎𝑛𝑠 𝐸𝑂≅ 𝐼𝑂
4. A diagonal that bisects each of the
noncongruent angles.
 Diagonal 𝐾𝑇 bisects ∠EKI and ∠ETI.
𝑇ℎ𝑖𝑠 𝑚𝑒𝑎𝑛𝑠 ∠𝐾𝑇𝐼 ≅ ∠𝐾𝑇𝐸 𝑎𝑛𝑑 ∠𝐼𝐾𝑇 ≅
∠𝐸𝐾𝑇

7. PROPERTIES OF KITE
AREA OF KITE = one-half product of diagonals
𝐴 =
1
2
𝑑1𝑑2
𝐴𝑟𝑒𝑎 =
1
2
𝐵𝐷 ∙ 𝐴𝐶

8. GIVEN : KITE ABCD . Identify the following:
a.Pairs of congruent sides
b.Diagonals
c. Pairs of congruent Angles
d.Non-congruent angles
e.If AC = 10, AE = ______
f. If ∠𝐴𝐵𝐶 = 88°, ∠𝐴𝐵𝐸 = _______
g.𝑚∠𝐶𝐸𝐵 =_____
AB, BC and DA, DC
AC and BC
∠𝐴, ∠𝐶
∠𝐵, ∠𝐷
5
44°
90°

9. GIVEN : KITE in the accompanying figure is a kite, If
𝑚∠𝐵𝐴𝐷 = 100, 𝑚∠𝐷 = 62, 𝑚∠𝐴𝐵𝐷 = 49, find the measure
of the following
a) 𝑚∠𝐷𝐵𝐶 =
b) 𝑚∠𝐴𝐵𝐶 =
c) 𝑚∠𝐴𝐶𝐵 =
d) 𝑚∠𝐶𝐷𝐵 =
e) 𝑚∠𝐵𝐸𝐴 =
f) 𝑚∠𝐷𝐸𝐴 =
g) 𝑚∠𝐴 + 𝑚∠B + m∠𝐶 + 𝑚∠𝐷 =
49°
98°
41°
31°
90°
90°
360°

10. LET’S TRY!
A. Given: KITE is a kite. Point O is the intersection of
diagonals KT and EI. Find the following:
1. 𝑚∠𝐾𝑂𝐼
2. |KO|
3. |OI|
4. |EI|
5. |KI|
6. |ET|
7. Area of the kite
5
27

11. Let’s Try
B. 𝐼𝑓 m∠KET = 11O°, 𝑚∠𝐸𝑇𝐼 = 80°, 𝑚∠𝐸𝐾𝑇 = 30°, then
8. 𝑚∠𝐼𝐸𝐾 = _____.
9. 𝑚∠𝑇𝐾𝐼 = _____.
10. 𝑚∠𝐸𝐾𝐼 = _____.
11. 𝑚∠𝐸𝐼𝐾 = _____.
12. 𝑚∠𝐼𝑇𝐾 = _____.
13. m∠KOE = _____.
14. 𝑚∠𝑇𝑂𝐼 = _____.
15. 𝑚∠𝐾𝐸𝑇 + 𝑚∠𝐸𝐾𝐼 + 𝑚∠𝐾𝐼𝑇 +
𝑚∠𝐼𝑇𝐸 = _____.
5