O
Show Me!
Given: Kite WORD with diagonals
WR and OD
W
R
Prove: WR is perpendicular bisector of OD
Proof:
D
1.
2.
3.
4.
Statements
Kite WORD
̅̅̅̅̅̅ ≅ 𝑊𝐷
̅̅̅̅̅ ≅ 𝑅𝐷
̅̅̅̅̅ ; 𝑂𝑅
̅̅̅̅
𝑊𝑂
̅̅̅̅̅̅ = 𝑊𝐷
̅̅̅̅̅ = 𝑅𝐷
̅̅̅̅̅ ; 𝑂𝑅
̅̅̅̅
𝑊𝑂
̅̅̅̅̅
̅̅̅̅̅
𝑾𝑹 ⊥ 𝑶𝑫
Reasons
1.
2.
3.
4.
Given
Definition of a kite
Definition of congruent segments
If a line contains two points each of
which is equidistant from the
endpoints of a segment, then the
line is the perpendicular bisector of
the segment.
E
Show Me!
Given: Kite ROPE
1
Prove: Area of a kite ROPE = 2 (𝑂𝐸)(𝑃𝑅)
P
R
W
Proof:
O
Statements
1. Kite ROPE
Reasons
1. Given
2. The diagonals of a kite are
perpendicular to each other.
̅̅̅̅
̅̅̅̅ ⊥ 𝑶𝑬
2. 𝑷𝑹
3. Area of kite ROPE = Area of △ 𝑂𝑃𝐸 +
Area of △ 𝑂𝑅𝐸
1
4. Area of △ 𝑂𝑃𝐸 = 2 (𝑂𝐸)(𝑃𝑊)
1
Area of △ 𝑂𝑅𝐸 = 2 (𝑂𝐸)(𝑊𝑅)
5. Area of kite ROPE
1
1
(𝑂𝐸)(𝑃𝑊)
+
(𝑂𝐸)(𝑊𝑅)
2
2
6. Area of kite ROPE
1
(𝑂𝐸)(𝑃𝑊 + 𝑊𝑅)
2
3. Area Addition Postulate
4. Area Formula for Triangles
5. Substitution
6. Associative Property
7. PW + WR = PR
1
8. Area of kite ROPE = 2 (𝑂𝐸)(𝑃𝑅)
7. Segment Addition Postulate
8. Substitution
L
Activity 17: Play a Kite
Given: Quadrilateral PLAY is a kite.
1. Given: PA = 12 cm; LY = 6 cm
Questions:
 What is the area of kite PLAY?
o 39 cm2
A
P
Y


How did you solve for its area?
o By multiplying the lengths of the two diagonals and dividing it by two.
What theorem justifies your answer?
o The area of a kite is half the product of the lengths of its diagonals.
2. Given: Area of kite PLAY = 135 cm; LY = 9 cm
Questions:
 How long is PA?
o 30 cm
 How did you solve for PA?
o By multiplying the area of kite PLAY and dividing it by the segment ̅̅̅̅
𝑳𝒀.
 What theorem justifies your answer?
o The area of a kite is half the product of the lengths.
QUIZ 3
̅
A. Refer to trapezoid EFGH with 𝐼𝐽
H
1. If IJ = x, HG = 8 and EF = 12,
what is the value of x?
I
 x = 10
2. If IJ = y +3, HG = 14, EF = 18,
What is the value of y? What is IJ?
E
 y = 13
 IJ = 16
3. If HG = x, IJ = 16 and EF = 22, what is the value of x?
 x = 10
4. If HG = y – 2, IJ = 20 and EF = 31, what is the value of y? What is HG?
 y = 11
 HG = 9
5. If HI = 10 and IE = x-4, what is the value of x? What is IE?
 x = 14
 IE = 10
B. Given isosceles trapezoid ABCD
1. Name the legs.
 ̅̅̅̅
𝑫𝑨, ̅̅̅̅
𝑪𝑩
2. Name the bases.
 ̅̅̅̅
𝑫𝑪, ̅̅̅̅
𝑨𝑩
3. Name the base angles.
 ∠𝑨, ∠𝑩
4. If m∠𝐴 = 70, what is m∠𝐵?
 m∠𝑩 = 70
5. If m∠𝐷 = 105, what is m∠𝐶?
A
 m∠𝑪 = 105
6. If m∠𝐵 = 2x-6 and m∠𝐴 = 82, what is x?
 x = 44
7. If m∠𝐶 = 2(y+4) and m∠𝐷 = 116, what is y?
 y = 54
8. If AC = 56 cm, what is DB?
 DB = 56
9. If AC = 2x+10 and DB = 4x-6, what is AC?
 AC = 26
10. If DB = 3y+7 and AC = 6y-8, what is DB?
 DB = 22
D
G
J
F
C
B
C. Consider kite KLMN on the right.
1. Name the pairs of congruent and adjacent sides.
̅̅̅̅̅ ≅ 𝑴𝑵
̅̅̅̅̅ and 𝑲𝑵
̅̅̅̅̅ ≅ 𝑲𝑳
̅̅̅̅
 𝑴𝑳
2. If LM = 6, what is MN?
 MN = 6
3. If KN = 10.5, what is KL?
 KL = 10.5
4. If LN = 7 cm and KM = 13 cm, what is the area?
 45.5 cm2
5. If the area is 96 cm2 and LN = 8 cm, what is KM?
 KM = 24
6. If m∠2 = 63, what is m∠3?
 m∠𝟑 = 27
7. If m∠3 = 31, what is m∠𝐿𝑀𝑁?
 m∠𝑳𝑴𝑵 = 62
8. If m∠5 = 22, what is m∠4?
 m∠𝟒 = 68
9. If m∠𝐿𝐾𝑁 = 39, what is m∠𝑀𝐾𝑁?
 m∠𝑴𝑲𝑵 = 19.5
10. If m∠4 = 70, what is m∠𝐾𝐿𝑁?
 m∠𝑲𝑳𝑵 = 70
M
N
L
K
Activity 18: You Complete Me!
1
P
A
R
A
L
L
E
L
O
G
R
9
A N
M
2
R E C T
H
O
4
M
T R
B
U
6
S
D
E
3
Q
U
A
A 5P E Z O I D
A
R
R
I
I A G O N A L
L
A
L
T
7
8
S Q U A R E
K
E
L
I
R
G L E
T
A
10
V E R T E X
L
DOWN:
1 – Quadrilateral ABCD where ̅̅̅̅
𝐴𝐵 ∥
̅̅̅̅, 𝐴𝐷
̅̅̅̅ ∥ 𝐵𝐶
̅̅̅̅
𝐶𝐷
̅ ≅
2 – Parallelogram FILM where ̅̅̅
𝐹𝐼 ≅ 𝐼𝐿
̅̅̅̅ ≅ 𝑀𝐹
̅̅̅̅̅
𝐿𝑀
3 – A polygon with two diagonals
5 – a condition where two coplanar lines
never meet
̅̅̅̅ ⊥
8 – quadrilateral PARK where 𝑃𝑅
̅̅̅̅
̅̅̅̅
̅̅̅̅
𝐶𝐷, 𝑃𝑅 ≠ 𝐴𝐾
A N G L
ACROSS:
2 – Quadrilateral HEAT where ∠𝐻 ≅ ∠𝐸 ≅
∠𝐴 ≅ ∠𝑇
4 – Quadrilateral KING where ̅̅̅
𝐾𝐼 ∥ ̅̅̅̅
𝑁𝐺 and
̅̅̅̅ is not parallel to 𝐼𝑁
̅̅̅̅
𝐾𝐺
̅̅̅̅ in quadrilateral TOUR
6 - 𝑅𝑂
7 – parallelogram ONLY were ∠𝑂 ≅ ∠𝑁 ≅
̅̅̅ ≅ ̅̅̅̅
∠𝐿 ≅ ∠𝑌 and ̅̅̅̅
𝑂𝑁 ≅ ̅̅̅̅
𝑁𝐿 ≅ ̅𝐿𝑌
𝑌𝑂
9 – formed by two consecutive sides of a
polygon
10 – U in quadrilateral MUSE
Activity 19: It’s Showtime!
B
A
F
S
N
O
KM
J
C
DE
R
T
Q
P
H
L
I
Quadrilateral
ABCD
EFGH
IJKL
MNOP
QRST
Specific Kind
Rhombus
Trapezoid
Square
Diamond
Rectangle
Questions:
1. Which quadrilateral is a rectangle? Why?
 Quadrilateral QRST. Because both pairs of opposite sides have equal slopes
and four pairs of consecutive sides have slopes whose product is –1.
2. Which quadrilateral is a trapezoid? Why?
̅̅̅̅ and ̅̅̅̅̅
 Quadrilateral EFGH. Because one pair of opposite sides (𝑬𝑭
𝑯𝑮) have
equal slopes.
3. Which quadrilateral is a kite? Why?
G

Quadrilateral MNOP. Because both pairs of opposite sides do not have equal
̅̅̅̅̅ and 𝑵𝑷
̅̅̅̅̅) produce a product of -1.
slopes and diagonals (𝑴𝑶
4. Which quadrilateral is a rhombus? Why?
 Quadrilateral ABCD. Because both pairs of opposite sides have equal slopes
and four pairs of consecutive sides do not produce a product of -1
5. Which quadrilateral is a square? Why?
 Quadrilateral IJKL. Because both pairs of opposite sides are have equal
slopes. Four pairs of consecutive sides produce a product of -1. And
diagonals also produce a product of -1.
Activity 20: Show More What We Got!
1. Given: Quadrilateral WISH is a parallelogram.
a. If m ∠W = x + 15 and m ∠S = 2x + 5, what is m ∠W?
 m ∠W = 25
b. If WI = 3y + 3 and HS = y + 13, how long is HS?
 HS = 18
the other side. What are its dimensions and how large is its area?
 11 cm by 17 cm = 187 cm2
d. What is the perimeter and the area of the largest square that can be formed from
rectangle WISH in 1.c.?
 Perimeter = 56 cm Area = 196 cm2
2. Given: Quadrilateral POST is an isosceles trapezoid with OS || PT. ER is its median.
a. If OS = 3x – 2, PT = 2x + 10 and ER = 14, how long is each base?
 PT = 18 units OS = 10 units
b. If m ∠P = 2x + 5 and m ∠O = 3x – 10, what is m ∠T?
 ∠T = 79 degrees
c. One base is twice the other and ER is 6 cm long. If its perimeter is 27 cm, how long is
each leg?
 7.5 cm
d. ER is 8.5 in long and one leg measures 9 in. What is its perimeter if one of the bases is
3 in more than the other?
 35 in
3. Given: Quadrilateral LIKE is a kite with LI ≅ IK and LE ≅ KE.
a. LE is twice LI. If its perimeter is 21 cm, how long is LE?
 LE = 7 cm
b. What is its area if one of the diagonals is 4 more than the other and IE + LK = 16 in?
 30 in2
c. IE = (x – 1) ft and LK = (x + 2) ft. If its area is 44 ft2, how long are IE and LK?
 IE = 8 ft LK = 11 ft