GEOMETRY Unit 7 - Schoolwires

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


The Number of Sides


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



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


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


If __________________

and ________________, then


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.


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)


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


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.


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 = ________


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


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.


• 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.


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)


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?


consecutive angles that are

supplementary?


diagonals that are perpendicular?


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)


Date: ________________________ Per: _______ Homework 5: Classifying Quadrilaterals

in the Coordinate Plane

EFGH is a _______________________________.


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


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.


• 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


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.


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


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


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 )


( 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 bisect

opposite angles.

• Four right angles.


Squares have ALL the

properties of parallelograms,

rectangles, and rhombi!

• Opposite sides parallel.

• Opposite sides congruent.

• Opposite angles congruent.

• Consecutive angles supplementary.


• 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.


• Base angles are congruent.

• Opposite angles are

supplementary.

• Exactly two pairs of

consecutive congruent sides.

• One pair of opposite

angles are congruent.


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.


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


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

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