Quadrilaterals:
Rectangles
Notes and Assignment
A rectangle is defined

as a parallelogram
Properties of the Sides:
Both pairs of opposite sides parallel
o
with four right angles

FH // EI and FE // HI
Both pairs of opposite sides congruent
o
FH  EI and FE  HI
F
Interior
angle
sum of
360
degrees.
H
Diagonals
create
congruent
right
triangles.
G
E



Properties of the Angles:
Both pairs of opposite angles congruent
o F  I and E  H
Consecutive angles are supplementary
E  I 180, I  H 180,
o
H  F 180, F  E 180
Four right angles
o mE  mI  m H  mF  90
I
Bisected
diagonals
create
isosceles
triangles.
Properties of the Diagonals:

Diagonals bisect each other
o

FG  GI and EG  GH
Diagonals are congruent
o
FI  EH
© ("Secondary Math Shop") 2013
Examples
Examples 1 - 9, PRST is a rectangle, find each angle if m1 = 50
40
1. m2 = ______
40
2. m3 = ______
50
3. m4 = ______
40
4. m5 = ______
40
5. m6 = ______
50
6. m7 = ______
P
1
80
8. m9 = ______
2
9
7
100
7. m8 = ______
3
80
9. m10 = ______
8
R
4
10
5
6
S
T
Examples 10 - 13, PRST is a rectangle, find the value of each variable.
10.
P
Four Right Angles
11.
7x - 4
R
P
Opposite sides congruent
R
(6y + 2)
7x  4  6x  4
x44
x8
T
8 x  10  90
8 x  80; x  10
(5x + 8)
Alternate Interior Angles 
(3x + 2)
S
6x + 4
5 x  8  3 x  2  90
S
T
6 y  2  3(10) 2
6 y  2  32
6 y  30; y  5
13.
12. PS = 6x + 3, RT = 7x - 2
P
P
R
R
Diangonals congruent
7x  2  6x  3
T
S
x23
x5
Diangonals bi sec t e. o.
2x - 4
2 x  4  36
36
T
S
2 x  40
x  20
© ("Secondary Math Shop") 2013
A rectangle is defined

as a parallelogram
Properties of the Sides:
Both pairs of opposite sides parallel
o
with ___________________

FH // EI and FE // HI
Both pairs of opposite sides congruent
o
FH  EI and FE  HI
F
Interior
angle
sum of
360
degrees.
H
G
E



Properties of the Angles:
Both pairs of opposite angles congruent
o F  I and E  H
Consecutive angles are supplementary
E  I 180, I  H 180,
o
H  F 180, F  E 180
Four right angles
o
I
Properties of the Diagonals:

Diagonals bisect each other
o

FG  GI and EG  GH
Diagonals are congruent
o
© ("Secondary Math Shop") 2013
A rectangle is defined

as a parallelogram
Properties of the Sides:
Both pairs of opposite sides parallel
o
with ___________________

Both pairs of opposite sides congruent
o
F
H
G
E



Properties of the Angles:
Both pairs of opposite angles congruent
o
Consecutive angles are supplementary
o
Four right angles
o
I
Properties of the Diagonals:

Diagonals bisect each other
o

Diagonals are congruent
o
© ("Secondary Math Shop") 2013
Examples
Examples 1 - 9, PRST is a rectangle, find each angle if m1 = 50
1. m2 = ______
2. m3 = ______
3. m4 = ______
4. m5 = ______
5. m6 = ______
6. m7 = ______
P
1
8. m9 = ______
2
9
7
7. m8 = ______
3
4
10
5
6
S
T
9. m10 = ______
8
R
Examples 10 - 13, PRST is a rectangle, find the value of each variable.
10.
P
11.
7x - 4
R
P
R
(6y + 2)
(5x + 8)
T
6x + 4
12. PS = 6x + 3, RT = 7x - 2
P
(3x + 2)
S
R
T
S
P
R
13.
2x - 4
36
T
S
T
S
© ("Secondary Math Shop") 2013
Name: _____________ANSWER KEY________________ Hour: _____________________ Date: _______
Questions 1 - 9, ABCD is a rectangle, find each angle if m1 = 36
1. m2 = ______
144
72
4. m5 = ______
18
2. m3 = ______
72
5. m6 = ______
A
72
3. m4 = ______
B
6
72
8. m9 = ______
4
7
36
6. m7 = ______
9
144
7. m8 = ______
3
18
9. m10 = ______
8 1
2
5
10
D
C
Questions 10 - 13, ABCD is a rectangle, with diagonals that intersect at E. Find the value of each variable.
2 x  6  36
2 x  30
x  15
x  2  14  3 x
4 x  2  14
4 x  12
x3
2 y  6  12
2 y  18
y9
3 y  11  26
3 y  15
y5
5 x  8  4 x  8  90
x  7  6x  8
9 x  90
7  5x  8
x  10
15  5 x
3 x
© ("Secondary Math Shop") 2013
Questions 14 - 19, MNOP is a rectangle, with diagonals that intersect at C. Find the value of each variable
or the missing part.
35
15
80
15
2 ( x  5)  4 x  60
2 x  10  4 x  60
10  2 x  60
70  2 x ; x  35
4 x  60  30  x
5 x  60  30
5 x  90 ; x  15
MN  4(15)  60  15
11
MO  4(35)  60  80
3
41
5 x  14  4 x  5  90
9 x  9  90
9 x  99 ; x  11
CMP  5 (11)  14  41
7
18
2 x  3  12  x
3 x  3  12
3x  9 ; x  3
NP  2 (12  3)  18
2
26
3 x  5  40  2 x
5 x  5  40
5 x  35 ; x  7
MOP  40  2(7)  26
28
18 x  8  70  4 x  90
14 x  62  90
14 x  28 ; x  2
OMN  18( 2)  8  28
© ("Secondary Math Shop") 2013
Name: __________________________________________ Hour: _____________________ Date: _______
Questions 1 - 9, ABCD is a rectangle, find each angle if m1 = 36
1. m2 = ______
4. m5 = ______
2. m3 = ______
5. m6 = ______
A
3. m4 = ______
B
6
8. m9 = ______
6. m7 = ______
9. m10 = ______
4
7
9
7. m8 = ______
3
10
8 1
2
5
D
C
Questions 10 - 13, ABCD is a rectangle, with diagonals that intersect at E. Find the value of each variable.
© ("Secondary Math Shop") 2013
Questions 14 - 19, MNOP is a rectangle, with diagonals that intersect at C. Find the value of each variable
or the missing part.
© ("Secondary Math Shop") 2013
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