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GEOMETRY7Unit
HONORS GEOMETRY
Unit 7 – Polygons & Quadrilaterals: TOPIC HOMEWORK
DAY 1 Interior & Exterior Angles of Polygons HW #1
DAY 2 Parallelograms HW #2
DAY 3
HW #3
DAY 4 Quiz 7-1
DAY 5 Rectangles
HW #4 DAY 6 Rhombi & Squares
HW #5 DAY 7 Quadrilaterals in the Coordinate Plane: Is it a Parallelogram, Rectangle, Rhombus, or Square?
HW #6
DAY 8 Quiz 7-2 None
DAY 9 Trapezoids
HW #7 DAY 10 Kites
DAY 11 Unit 7 Review
DAY 12 UNIT 7 TEST
Main Ideas/Questions Notes/Examples
A polygon is a _______________ figure formed by three or more
____________ ___________________, called ______________.
Sum of the
Measures
The sum of the measures of the interior angles in any polygon can be determined by the number of triangles that can be drawn within the
polygon. Complete the table below and look for a pattern to find the sum of the degrees in any polygon.
Polygon Picture # of Sides # of Triangles Sum of Interior’s
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon X
Octagon X
Nonagon X
Decagon X
Angle Sum
If n represents the number of sides of a polygon, then the sum of the interior angle, S, can be found using the formula:
______________________________________
Find the sum of the measures of the interior angles in each polygon.
1. 15-gon 2. 21-gon
3. 48-gon 4. 36-gon
Section 7.1 Interior & Exterior Angles of Polygons
1
The measure of a single interior angle in a regular polygon can be be found by dividing the sum of the interior angle
measures, S, by the number of sides, n.
Find the measure of each interior angle in the following polygons.
5. regular pentagon 6. regular 18-gon
Sum of the
Measures
Exterior angles are supplementary to their adjacent interior angle. Find the measure of each exterior angle on the polygons below,
then give the sum of all exterior angle measures.Triangle: Quadrilateral:
Pentagon: Hexagon:
What can you conclude about the sum of the exterior angles measures of
a polygon?
7. What is the measure of eachexterior angle of a regularhexagon?
8. What is the measure of eachexterior angle of a regular24-gon?
9. If the exterior angle of a regularpolygon measures 12°, howmany sides does the polygonhave?
10. If the exterior angle of a regularpolygon measures 40°, howmany sides does the polygonhave?
79
61 40
98 121
87
130 104
71
124 76
89
117 123
129
115 112
124
Sum of Exterior
Angles Measures:
__________
Sum of Exterior
Angles Measures:
__________
Sum of Exterior
Angles Measures:
__________
Sum of Exterior
Angles Measures:
__________
2
Sum of the INTERIOR Angle Measures: Sum of the EXTERIOR Angle Measure:
Interior Angle Measure
of a Regular Polygon:
Exterior Angle Measure
of a Regular Polygon:
The Number of Sides
of a Regular Polygon:
1. What is the sum of the measures of the interior
angles of a pentagon?
2. What is the sum of the measures of the interior
angles of a 27-gon?
3. What is the measure of each interior angle of
a regular octagon?
4. What is the measure of each interior angle of
a regular 20-gon?
5. Five angles of a hexagon measure 119°, 129°, 104°, 139°, and 95°. What is the measure of the
sixth angle?
6. The sum of the interior angles of a polygon is 1620°. How many sides does the polygon have?
7. The sum of the interior angles of a polygon is 3960°. How many sides does the polygon have?
8. What is the sum of the measures of the exterior
angles of a nonagon?
9. What is the measure of each exterior angle of a
regular 20-gon?
more practice with
3
10. If the exterior angle of a regular polygon
measures 9°, how many sides does the
polygon have?
11. If the interior angle of a regular polygon
measures 108°, how many sides does the
polygon have?
12. Find the value of x. 13. Find the value of x.
14. Solve for x.
15. Find mB.
16. If the figure below is a regular polygon, find the value of x.
17. Find the value of x.
79
110
55
x
140
142 148
136
150
x
110 (8x – 1)
(5x + 36)
116 (7x + 19)
(6x – 2)
A
B
C
D
(14x – 11)
(8x + 7) (5x + 18)
(10x + 13)
(10x + 4)
(4x + 1) (9x – 6)
(4x + 9)(5x + 4)
(7x + 4)
4
Name: ___________________________________ Unit 7: Polygons & Quadrilaterals
Date: ________________________ Per: _______ Homework 1: Angles of Polygons
1. What is the sum of the measures of the interior angles of an octagon? ___________
2. What is the sum of the measures of the interior angles of a 25-gon? ___________
3. What is the measure of each interior angle of a regular hexagon? __________
4. What is the measure of each interior angle of a regular 16-gon? __________
5. What is the sum of the measures of the exterior angles of a decagon? __________
6. What is the measure of each exterior angle of a regular 30-gon? __________
7. An exterior angle of a regular polygon measures 22.5°. How many sides does it have? _______
8. An interior angle of a regular polygon measures 170°. How many sides does it have? _______
9. If the sum of the measures of the interiorangles of a polygon is 1980°, how manysides does the polygon have?
10. If the sum of the measures of the interiorangles of a polygon is 5400°, how manysides does the polygon have?
11. The measure of the seven angles in a nonagon measure 138°, 154°, 145°, 132°, 128°, 147°,and 130°. If the two remaining angles are equal in measure, what is the measure of eachangle?
12. Find the value of x. 13. Find the value of x.
87
105 135
92
x
x
141
158
116
124 136
132
129
** This is a 2-page document! **
5
14. Find the value of x.
15. Find the value of x.
16. Find mV.
17. If the figure below is a regular polygon, find the value of x.
18. Find mBCA.
(3x + 31)
(4x + 15)
(6x – 8) 120
(7x – 64)
135 (5x – 4)
(8x – 1)
(10x + 6)
(13x – 2)
71
(9x – 18)
S T
U
VW
X
(5x + 8)
111
(9x – 19)
(7x + 3)
128
A
B
C
(5x + 12)
(9x + 1)
(10x – 37)
6
Main Ideas/Questions Notes/Examples
Properties of
Definition of a Parallelogram:
Other important properties of parallelograms:
1
2
3
4
Directions: Each quadrilateral below is a parallelogram. Find the missing measures.1. 2.
3. 4.
5. Given XY = 15, WX = 22, ZX = 32, WT = 10, mWZY = 62, mWXT = 27, and mZWT = 77.
6. Given mGHF = 34, mHJF = 124, and mFKJ = 79.
A B
C D
68 8
15 AD = ________
DC = ________
mA = _______
mB = _______
mC = _______
J
K
L M
127 29
21
JK = ________
KL = ________
mJ = _______
mK = _______
mM = _______
UT = _______
ST = _______
VS = _______
VT = _______
mDEC = ________
mCDE = ________
mECD = ________
mDFE = ________
W
T
X
Y Z
F
G H
J
K
mTZY = ________
mXYZ = ________
mXWT = ________
mXYT = ________
ZW = _______
ZY = _______
TX = _______
WY = _______
G
71
C
D
E
F
21
*mFED = 134
7
R S
T U
V 18
27
*RT = 30
mGFJ = ________
mFGH = ________
mHFJ = ________
mHKJ = ________
mJGH = ________
mFGJ = ________
mFHJ = ________
mGJF = ________
Section 7.2 Parallelograms
7
7. Solve for x. 8. Find YZ.
9. If TV = 74 and WV = 4x + 1, solve for x. 10. If NS = 2x + 7 and SQ = 5x – 23, find NQ.
11. Find mB. 12. Find mR.
13. If mKLH = 134, solve for x. 14. If mABC = 115, find mADB.
P
Q
R
S
(3x + 5)
(8x – 12)
L M
N P 5x + 7
9x – 25
B C
D A
(4x + 11)
(6x – 15)
W
X
Y
Z 19x – 31
11x + 1
S
T U
V
W
N
P Q
R
S
H
J K
L
N
(4x + 9)
25
A
B
C
D
(6x – 11)
(4x + 6)
8
SET 1: Use the distance formula to determine if the figure is a parallelogram.1. A(-7, 4), B(1, 2) , C(9, -8), D(1, -6)
2. P(-4, 2), Q(6, 4), R(11, -2), S(2, -3)
PROVING PARALLELOGR
AMS in the Coordinate PlaneProve both pairs of opposite sides are congruent. Use….
Prove both pairs of opposite sides are parallel. Use….
Prove one pair of opposite sides are congruent and parallel. Use….
A B
C D
If __________________
and ________________, then
ABCD is a parallelogram.
A B
C D
A B
C D
If __________________
and ________________, then
ABCD is a parallelogram.
If __________________
and ________________, then
ABCD is a parallelogram.
9
SET 2: Use the slope formula to determine if the figure is a parallelogram.3. W(-7, -4), X(1, -6), Y(5, -13), Z(1, -12)
4. E(0, 8), F(6, 10), G(2, 0), H(-4, -2)
SET 3: Use the distance formula AND slope formula to determine if the figure is a parallelogram. 5. J(-9, -2), K(-5, 1), L(1, -4), M(-3, -7)
6. S(1, 5), T(10, 7), U(14, 1), V(-3, -1)
10
Directions: If each quadrilateral below is a parallelogram, find the missing measures.1.
2.
3. Given PQ = 24, PS = 19, PR = 42, TQ =10, mPQR = 106, mQSR = 49, and mPRS = 35.
4. Find KL. 5. If AC = 8x – 14 and EC = 2x + 11, solve for x.
6. Solve for x. 7. Find mV.
Name: ___________________________________ Unit 7: Polygons & Quadrilaterals
Date: ________________________ Per: _______ Homework 2: Parallelograms
K
L
M
N
31 45
119
MN = ________
KN = ________
mK = _______
mL = _______
mM = _______ E
C D
F
15
10 7
*FD = 22
G
CF = _______
FE = _______
CE = _______
GD = _______
P
Q
R
S
T
mQRS = ________
mPQS = ________
mRPS = ________
mPSQ = ________
QR = _______
SR = _______
PT = _______
SQ = _______
J
K L
M
7x – 2
12x – 22
A B
C D
E
Q
R
S
T
(3x + 5)
(9x – 17)
V W
X Y
(10x – 27)
(2x + 29)
** This is a 2-page document! **
11
8. If mBCD = 51, solve for x. 9. If mVST = (5x + 23) and mVUT =(8x – 49), find mSVT.
Directions: Determine whether the quadrilateral is a parallelogram using the indicated method.10. Q(-10, -2), R(1, -1), S(1, -7), T(-11, -8) (Distance Formula)
11. K(2, 7), L(6, 12), M(13, 13), N(9, 8) (Slope Formula)
12. D(-5, -6), E(5, 2), F(4, -4), G(-6, -12) (Distance & Slope Formulas)
E
B C
D
F
(14x + 4)
55
20
12
Main Ideas/Questions Notes/Examples
Properties of
Rectangles have the same properties of parallelograms:
• Opposite sides are congruent.• Opposite sides are parallel.• Opposite angles are congruent.• Consecutive angles are supplementary.• Diagonals bisect each other.
1
2
Directions: Each quadrilateral below is a rectangle. Find the missing measures.1. 2.
3. 4.
5. Given DB = 42, AD = 26, and mDAE = 52.
QR = _______
SR = _______
SQ = _______
PR = _______
QT = _______
W
AC = _______
BD = _______
BE = _______
AB = _______
BC = _______
mMJK = ________
mMJL = ________
mJLK = ________
mKML = ________
mMNL = ________
P Q
R S
T
24
10
A B
C D
E
15
27
J K
L M
N
27 64
W X
Y Z
V
mXWY = ________
mYXZ = ________
mWVZ = ________
mXWZ = ________
mXZY = ________
A B
C D
E
AC = ________
EB = ________
BC = ________
AB = ________
mADC= ________
mABD = ________
mBCA = ________
mDEC = ________
Section 7.3 Rectangles
13
6. Find EF. 7. If RT = 5x – 14 and US = 2x + 10, find VT.
8. If JM = x + 17 and MK = 5x – 23, find JL. 9. If VW = 9x – 11 and SU = 16x – 12, find WT.
10. Find mBCE. 11. Find mJHI.
12. Find mXZW. 13. Solve for x.
C D
E F
3x + 5
7x – 39
R S
T U
V
K L
H
M
S T
U V
W
A B
C D
E
(7x + 5)
(11x – 3)
I J
G
K
(3x + 2)
(12x – 17)
W X
Y Z
R
(5x – 8)
(x + 20)
D E
F G
H
134 (5x + 7)
14
Directions: If each quadrilateral below is a rectangle, find the missing measures.
1. 2.
3.
4. 5.
6. Find WZ. 7. If SQ = 11x – 26 and PR = 5x + 28, find PR.
Name: ___________________________________ Unit 7: Polygons & Quadrilaterals
Date: ________________________ Per: _______ Homework 3: Rectangles
V W
X Y
Z
31
19
10
VW = _______
WX = _______
YW = _______
ZX = _______
VX = _______
D E
F G
H
11
*GH = 14
GF = _______
GE = _______
DF = _______
HF = _______
DG = _______
59 1 2
3 4 5
6 7
8 9 10
11
A B
C D
E 16
mBCD = ________
mABD = ________
mCBE = ________
mADE = ________
mAEB = ________
mDEA = ________
H J
K L
M
126
mJMK = ________
mJKH = ________
mHLK = ________
mHJ L= ________
mLHK = ________
mJLK = ________
W X
Y Z
7x – 6 3x + 14
P Q
R S
T
m1 = ________
m2 = ________
m3 = ________
m4 = ________
m9 = ________
m10 = ________
m11 = ________
m5 = ________
m6 = ________
m7 = ________
m8 = ________
** This is a 2-page document! **
15
8. If AE = 6x – 55 and EC = 3x – 16, find DB. 9. If LO = 15x + 19 and QN = 10x + 2, find PN.
10. If DE = 4x + 1, EB = 12x – 31, and CD = 28, find AD.
11. Find mGJK. 12. Find mADE.
13. Find mVWZ. 14. Find mDHG.
A B
C D
E
O P
L
Q
A B
C D
E
I J
G
K
(5x + 8)
(7x – 16)
A B
C D
E
(4x + 15)
(13x + 7)
V W
X Y
Z
(5x – 12)
(2x – 3)
F G
D
H
(9x + 3)
(14x – 27)
16
Main Ideas/Questions Notes/Examples
Properties of
RHOMBI
Rhombi have the same properties of parallelograms:
• Opposite sides are congruent.
• Opposite sides are parallel.
• Opposite angles are congruent.
• Consecutive angles are supplementary.
• Diagonals bisect each other.
1
2
3
Directions: Each quadrilateral below is a rhombus. Find the missing measures.
1. JK = 12 and JN = 7 2. EF = 23 and DF = 40
3. RT = 22 and US = 18 4.
5. ZY = 34, WY = 38, and mZXY = 34.
JM = ________
JL = _________
MN = ________
MK = ________
m1 = ________
m2 = ________
m3 = ________
m4 = ________
J K
L M
N D
E
F
G
H
R
S
T
U
V
GF = ________
HF = ________
GH = ________
GE = ________
VT = ________
UV = ________
RS = ________
ST = ________ 38
1 2
3
4 5
6 7
8
m5 = ________
m6 = ________
m7 = ________
m8 = ________
W X
Y Z
V
WZ = ________
VY = ________
ZV = ________
ZX = ________
mWXZ = ________
mWVZ = ________
mZYW = ________
mXYW = ________
W Plus these!
Section 7.4 Rhombi & Squares
17
Properties of
SQUARES
A square has ALL the properties of a
parallelogram, rectangle, and rhombus!
6. If ABCD is a square and AD = 11, find each missing value.
7. If PQRS is a square and TR = 17, find each missing value.
8. If MNOP is a rhombus, find MP. 9. If CDEF is a rhombus, find mFED.
10. If STUV is a square with SW = 2x + 13
and WU = 8x – 41, find VT.11. If FGHI is a square, solve for x.
C D
E F
G
(8x – 20)
(5x + 1)
M N
O P
Q
3x + 7
9x – 77
S T
U V
W
F G
H I
J
(7x + 3)
• Opposite sides are congruent.
• Opposite sides are parallel.
• Opposite angles are congruent.
• Consecutive angles are
supplementary.
• Diagonals bisect each other.
• Four right angles.
• Diagonals are congruent.
• Four congruent sides.
• Diagonals are perpendicular.
• Diagonals bisect opposite angles.
A B
C D
E
P Q
R S
T
BC = ________
AC = ________
BD = ________
EC = ________
mDAB = ________
mAEB = ________
mCBD = ________
mBAC = ________
PR = ________
QS = ________
QT = ________
PQ = ________
mPRS = ________
mSTR = ________
mPSR = ________
mQPR = ________
18
Directions: If each quadrilateral below is a rhombus, find the missing measures.
1. UV = 8 and WX = 5
2. BC = 28 and BD = 32
3. MK = 24, JL = 20, and mMJL = 50
4. Find PQ. 5. Find mHGI.
6. Find mADB. 7. If mXYZ = 136, solve for x.
Name: ___________________________________ Unit 7: Polygons & Quadrilaterals
Date: ________________________ Per: _______ Homework 4: Rhombi and Squares
T U
V W
X
TU = ________
WU = ________
TX = ________
TV = ________
B
C
D
E
F
CD = ________
FD = ________
EF = ________
EC = ________
J K
L M
N
NK = ________
NL = ________
ML = ________
JM = ________
mKNL = ________
mKJL = ________
mMLK = ________
mJKM = ________
mJML = ________
N P
Q R
S
9x – 32
5x + 16
F G
H I
J
(7x – 1)
(4x + 3)
(13x – 16)
(9x + 4)
A B
C D
E
W X
Y Z
R
(10x – 8)
** This is a 2-page document! **
19
8. If DE = 16x – 3, EF = 9x + 11, and DF = 52, find HG.
Directions: If each quadrilateral below is a square, find the missing measures.
9. 10.
11. 12. Solve for x.
13. Which quadrilaterals always have
diagonals that are congruent?
14. Which quadrilaterals always have
consecutive angles that are
supplementary?
15. Which quadrilaterals always have
diagonals that are perpendicular?
16. Which quadrilaterals always have
diagonals that bisect each other?
D
E
F
G
H
S T
U V
W 15
VU = ________
SU = ________
TV = ________
SW = ________
L M
N O
P
*LN = 46
OM = ________
PN = ________
ON = ________
MN = ________
D E
F G
H
mEFG = ________
mGDH = ________
mFEG = ________
mDHG = ________
P Q
R S
T
(6x – 21)
❑ Parallelograms
❑ Rectangles
❑ Rhombi
❑ Squares
❑ Parallelograms
❑ Rectangles
❑ Rhombi
❑ Squares
❑ Parallelograms
❑ Rectangles
❑ Rhombi
❑ Squares
❑ Parallelograms
❑ Rectangles
❑ Rhombi
❑ Squares
20
Directions: Given the vertices, determine the quadrilaterals most specific classification.
1 A(9, -4), B(8, -2), C(2, -5), D(3, -7)
To classify a quadrilateral as a parallelogram, rectangle, rhombus, or square:
➢ Step 1: __________________________________________________________________________
➢ Step 2: __________________________________________________________________________
ABCD is a _______________________________.
CASE 1
(Parallelogram)
Opposite sides are congruent and
diagonals are NOT congruent.
CASE 2
(Rectangle)
Opposite sides are congruent and
diagonals are congruent.
CASE 3
(Rhombus)
All four sides are congruent and
diagonals are NOT congruent.
CASE 4
(Square)
All four sides are congruent and
diagonals are congruent.
Section 7.5 Quadrilaterals in the Coordinate Plane
21
2 Q(-2, -7), R(1, -5), S(4, -7), T(1, -9)
3 J(5, -1), K(8, 2), L(11, 10), M(8, 7)
QRST is a _______________________________.
JKLM is a _______________________________.
22
4 W(-4, -3), X(1, -2), Y(2, -7), Z(-3, -8)
5 D(-5, 9), E(-3, 6), F(-6, -2), G(-8, 1)
WXYZ is a _______________________________.
DEFG is a _______________________________. 23
Quadrilaterals in the Coordinate Plane Directions: Use your knowledge of slope, distance, midpoint, and the properties of quadrilaterals to answer the following questions. 1. On parallelogram PQRS below, if P is located
at (-1, 6) and S is located at (-7, -3), what isthe slope ofQR ?
2. On rectangle ABCD below, if A is located at(3, 4) and B is located at (7, 6), what is theslope of BC ?
3. On rhombus WXYZ, if W is located at (-5, -2)and Y is located at (3, -2), what is the slope ofXZ ?
4. On square JKLM below, if J is located at(-2, 5) and K is located at (2, 2), what is theslope of LK ?
5. On parallelogram STUV below, if S is locatedat (-4, 1) and T is located at (5, 3), what isthe length of VU ?
6. On square PQRS below, if Q is located at(7, 0) and R is located at (5, -8), what isthe length of SR ?
7. On rectangle DEFG below, if D is located at(-1 -1) and F is located at (4, -8), what is thelength ofGE ?
8. On parallelogram ABCD below, if A(1, 1),B(8, 5), C(5, -5) and D(-2, -9), what arethe coordinates of point E?
P Q
R S
A
B
C
D
J
K
L
M
S
V
U
T
A
B
C
D
E
D E
F G
Q
S
P
W
X
Y
Z
24
Directions: Given the vertices, determine the quadrilaterals most specific classification:
Parallelogram, Rectangle, Rhombus, or Square. Justify your answer using the distance formula.
1. S(-9, 14), T(1, 10), U(-3, 0), V(-13, 4)
2. E(-7, -4), F(2, -3), G(0, -7), H(-9, -8)
Name: ___________________________________ Unit 7: Polygons & Quadrilaterals
Date: ________________________ Per: _______ Homework 5: Classifying Quadrilaterals
in the Coordinate Plane
EFGH is a _______________________________.
** This is a 2-page document! **
STUV is a _______________________________.
25
3. A(-5, 8), B(-2, 14), C(12, 7), D(9, 1)
4. K(5, -3), L(7, 1), M(9, -3), N(7, -7)
ABCD is a _______________________________.
KLMN is a _______________________________.
26
Main Ideas/Questions Notes/Examples
NON-ISOSCELES Trapezoids
ISOSCELES Trapezoids
Isosceles trapezoids have the same properties as
non-isosceles trapezoids, plus these:
Directions: Find each missing value on the trapezoids below.
1. 2.
3. Solve for x. 4. Find mR.
5. DEFG is an isosceles trapezoid. 6. TUVW is an isosceles trapezoid.
7. 8.
Properties of Non-Isosceles Trapezoids:
• Only O NE pair of opposite sides are parallel.
• Consecutive angles between parallel lines
are supplementary.
• Non-parallel sides (legs) are congruent.
• Diagonals are congruent.
• Base angles are congruent.
• Opposite angles are supplementary.
J K
L M
87
51
mK = _________
mM = _________
A B
C D
3162
mC = _________
mD = _________
mQ = _________
mR = _________
mS = _________
mW = _________
mY = _________
mZ = _________
D E
F G
DG _________
DF _________
T U
V W
T _________
U _________
112
P Q
R S
47 W X
Y Z
(8x + 6) 54
P Q
R S
(12x + 3)
(7x – 13)
Section 7.6 Trapezoids
27
9. If MNOP is an isosceles trapezoid, MP = 16x – 13, NO = 9x + 8, PN = 5y + 19, and
MO = 12y – 37, solve for x and y.
10. If ABCD is an isosceles trapezoid, find each missing angle.
11. If JKLM is an isosceles trapezoid, find each missing angle.
12. If WXYZ is an isosceles trapezoid, find each missing angle.
13. If CDEF is an isosceles trapezoid, find each missing angle.
14. If STUV is an isosceles trapezoid, find each missing angle.
mW = _________
mX = _________
mY = _________
mZ = _________
M N
O P
mA = _________
mB = _________
mC = _________
mD = _________ (2x + 27) (5x – 12)
A B
C D
(10x + 5)
(6x – 1)
W X
Y Z
(4x + 17)
(10x – 33) J K
L M
mJ = _________
mK = _________
mL = _________
mM = _________
(21x – 16) (18x + 5) C D
E F
(14x – 25)
S T
U V
(3x + 1)
mC = _________
mD = _________
mE = _________
mF = _________
mS = _________
mT = _________
mU = _________
mV = _________
28
Main Ideas/Questions Notes/Examples
MIDSEGMENT
of a TRAPEZOID
The midsegment of a trapezoid connects the midpoints of the legs:
Directions: Use the trapezoid above for questions 1-4.
1. If AB = 14 and DC = 26, find EF. 2. If AB = 7 and DC = 31, find EF.
3. If EF = 22 and DC = 38, find AB. 4. If AB = 41 and EF = 47, find DC.
5. For trapezoid PQRS, Y and Z are midpoints of the legs. Find YZ.
6. For trapezoid GHJK, L and M are midpoints of the legs. Find KJ.
7. For trapezoid WXYZ, U and V are midpoints of the legs. Find UV.
If EF is the midsegment of trapezoid ABCD, then:
• ___________________________________
• ____________________________________ D
E
A B
F
C
P Q
R S
Y Z
38
x + 14
5x – 19
G H
M
K
L
J
25
6x – 1
2x + 11
W X
Y Z
U V
x + 7
8x – 3
6x + 5
29
Directions: If each quadrilateral below is a trapezoid, find the missing measures.
1. 2.
3. 4.
5. Solve for x. 6. Find mB.
7.
8.
Name: ___________________________________ Unit 7: Polygons & Quadrilaterals
Date: ________________________ Per: _______ Homework 6: Trapezoids
mC = _________
mE = _________
Q
R S
T 91
27
mQ = _________
mS = _________
mJ = _________
mL = _________
mM = _________ W
X
Y Z
146
mW = _________
mX = _________
mZ = _________
U V
T
139
(14x – 15)
(6x + 20) (8x – 16) M N
O P
mM = _________
mN = _________
mO = _________
mP = _________
(8x – 2)
(13x – 7) W X
Y Z
mW = _________
mX = _________
mY = _________
mZ = _________
A B
C D
(9x + 2)
(5x – 4)
J K
L M
83
C D
E F
134
79
** This is a 2-page document! **
30
9.
10. If EFGH is an isosceles trapezoid, EH = 4x – 27, FG = x + 9, EG = 3y + 19, and FH = 11y – 21,
solve for x and y.
11. Find WX. 12. Find AB.
13. Find ML.
14. Find GH.
15. Find RS.
E F
G H
(25x – 14)
J K
L M
(7x + 2) mJ = _________
mK = _________
mL = _________
mM = _________
P Q
R S
W X
27
39
A B
C D
M N 22
29
J K
L M
N P 45
10x – 12
3x + 11
5x + 1
B C
E F
G H
19
9x – 3
R S
W
U
V
T
3x + 5
6x – 37
2x + 15
31
Main Ideas/Questions Notes/Examples
Properties of
KITES
A kite is a quadrilateral with the following properties:
Directions: If each quadrilateral below is a kite, find the missing values.
1. 2.
3. 4.
5. 6.
7. If WX = 14 and WR = 8, find RZ. 8. If AC = 38 and ED = 41, find CD.
mB = _________
mD = _________
mJ = _________
mK = _________
• Exactly two pairs of consecutive congruent sides.
( ADAB and DCBC )
• One pair of opposite angles are congruent.
( ADCABC )
• Diagonals are perpendicular.
( BDAC ⊥ )
A
B
C
D
E
B
A C
D
85 43 J
K
L
M
82
71
P Q
R
S
T
37
mPTQ = _________
mPQT = _________
mQRT = _________
D F
G
E
H 59
mGDE = _________
mDEH = _________
mDGH = _________
m1 = _________
m2 = _________
m3 = _________
m4 = _________
m5 = _________
m6 = _________
m7 = _________
73
46 1
2 3
4 5
6 7
52
65
1
2 3
5
4 6
7
m1 = _________
m2 = _________
m3 = _________
m4 = _________
m5 = _________
m6 = _________
m7 = _________
W Y
Z
X
R
A B
C
D
E
Section 7.7 Kites
32
9. If RS = 10 and RU = 9, find QS. 10. If GF = 15 and CG = 23, find CD.
11. Solve for x. 12. Find mL.
13. Solve for x. 14. Find mSTV.
15. Find mFGJ. 16. Find mNQP.
B
A C
D
109
(5x + 14) (3x + 8)
Q
R
S
T
U
C
D
E
F
G
(7x + 22)
S
T
U
V
(13x – 32)
N
K
L M
(5x + 23)
(8x – 31)
I
F
G
H
J
(5x – 1) (2x + 11)
U
R
S
T
V
(9x + 1)
(23x – 7)
N
O
P
Q R
(11x – 23)
(4x – 7)
33
• Four congruent sides.
• Diagonals are perpendicular.
• Diagonals bisect
opposite angles.
• Four right angles.
• Diagonals are congruent.
Squares have ALL the
properties of parallelograms,
rectangles, and rhombi!
• Opposite sides parallel.
• Opposite sides congruent.
• Opposite angles congruent.
• Consecutive angles supplementary.
• Diagonals bisect each other.
• Only ONE pair of opposite sidesare parallel (called bases).
• Consecutive angles
are supplementary.
Midsegment of a Trapezoid:A midsegment of a trapezoid
connects the midpoints of the legs.
This segment is equal to the
average of the two bases.
• Non-parallel sides
(legs) are congruent.
• Diagonals are congruent.
• Base angles are congruent.
• Opposite angles are
supplementary.
• Exactly two pairs of
consecutive congruent sides.
• One pair of opposite
angles are congruent.
• Diagonals are perpendicular.
QUADRILATERALS
34
Directions: If each quadrilateral below is a kite, find the missing measures.
1. 2.
3. 4. Given: mABC = 70 and mADC = 46.
5. If QR = 13 and PT = 8, find QT. 6. If KM = 52 and NL = 33, find LM.
7. If XZ = 46 and WR = 21, find WX. 8. If DE = 15 and EH = 11, find DF.
Name: ___________________________________ Unit 7: Polygons & Quadrilaterals
Date: ________________________ Per: _______ Homework 7: Kites
mF = _________
mH = _________
mU = _________
mV = _________
E F
G
H
31
87
T
U
V
W 65
91
18
43
1
4
2
3 5
6
7
m1 = ________
m2 = ________
m3 = ________
m4 = ________
m5 = ________
m6 = ________
m7 = ________
m8 = ________
m9 = ________
A
B
C
D
1
2 3
4 5
6 7
8 9
m1 = _________
m2 = _________
m3 = _________
m4 = _________
m5 = _________
m6 = _________
m7 = _________
P Q
R
S
T J L
M
K
N
D
E
F
G
H
W X
Y
Z
R
** This is a 2-page document! **
35
9. If NK = 7x – 1, NM = 10x – 13, and KM = 24, find NP.
10. Solve for x. 11. Find mS.
12. Solve for x. 13. Find mEDC.
14. Find mRST. 15. Find mHIF.
Q
R
S
T
(4x + 35) (8x – 9)
K
L
M
N P
C
D
A B
(8x – 27)
(3x + 58)
W
X
Y
Z (17x + 3)
(12x – 9)
96
B
A C
D
E
(9x – 1)
(2x + 13)
U
R
S
T
V
(4x – 19)
(3x + 25)
I
F
G
H
J
(2x + 6)
46
(7x + 3)
36