Name
Class
Date
Practice 6-1
Classifying Quadrilaterals
Determine the most precise name for each quadrilateral.
1.
y 4
2. A (3, 3)
E (2, 3) 4
B (7, 3)
y F (1, 3)
2
2 O D (1, 0)
O
6 4
10 x
C (5, 0)
H (2, 2)
2
4
6
x
G (1, 2)
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4
Judging by appearance, classify each quadrilateral in as many ways as possible.
3.
4.
5.
6.
7.
8.
Algebra Find the values of the variables. Then find the lengths of the sides of each quadrilateral.
9. rhombus ABDC A
10. parallelogram LONM
2x 3
18 x
C
3x 10 x4
O 2m 8 N
B
D
s 1
5m 2
L 3m 1 M
11. square FGHI F
3f 2
g6
I
G 2g 5
5f 8
H
Determine the most precise name for each quadrilateral with the given vertices.
12. A(1, 4), B(3, 5), C(6, 1), D(4, 0)
13. W(0, 5), X(3, 5), Y(3, 1), Z(0, 1)
14. A(-2, 4), B(2, 6), C(6, 4), D(2, -3)
15. P(-1, 0), Q(-1, 3), R(2, 4), S(2, 1)
Geometry Chapter 6
Lesson 6-1 Practice
1
Name
Class
Date
Practice 6-2
Properties of Parallelograms
Find the value of x in each parallelogram.
2.
15
3. x4
x
28 3x 2
2x 4
6.
7. x = EG
4x 4
B
8. IK = 35
E
x
F
6x 22 H
D
G
J
L
C
If AE ≠ 17 and BF ≠ 18, find the measures of the sides of parallelogram BNXL.
4x 3
I
4
A
K
B
9. BN
D
10. NX
I
11. XL
M
12. BL
Q
R
V
W
E
C
F J
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5. AC = 24 A
4x 10
4.
10
G
H
K
L
N
O S
P
T
U
X
Y
Find the measures of the numbered angles for each parallelogram.
13.
14.
1
1
80
17.
15.
2 140
2 50 1
19. 1
3
75
16.
2
3
3
40 47 72
22 45
1 2
2
1
50 2
3
1
3
18.
115
110
20.
113
3
1
3
82
2 30
50
4
Find the length of TI in each parallelogram.
21.
T
I
22. OR = 78 IO I
18
23. TR = 14, ME = 31 O
T
M
24. IE = 6, GT = 8 R
T I
R E
16
L
T
40
R
G E
2
Lesson 6-2 Practice
E
I
Geometry Chapter 6
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1.
Name
Class
Practice 6-3
Date
Proving That a Quadrilateral Is a Parallelogram
State whether the information given about quadrilateral SMTP is sufficient to prove that it is a parallelogram.
S
1. SPT SMT
2. SPX TMX, TPX SMX
3. SM PT, SP MT
4. SX XT, SM PT
5. PX MX, SX TX
6. SP MT, SP 6 MT
M X
P
T
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Algebra Find the values of x and y for which the figure must be a parallelogram. M
7.
4x 20
A
x 2x 14
I
x 26
P
M (12y 8)
5x 4 2y
I
6x 9
7y
9. I
M
8.
A P
P
(2x)
(5y 2) A
Algebra Find the value of x. Then tell whether the figure must be a parallelogram. Explain your answer.
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10.
3x 2
11.
(2x 25)
(x 30)
x4
(4x 10)
12.
(x 15)
50
2x 4
(2x) (3x 15)
2x 6
(2x)
Decide whether the quadrilateral is a parallelogram. Explain your answer.
13.
14.
15.
16.
17.
18.
19.
20.
Geometry Chapter 6
Lesson 6-3 Practice
3
Name
Class
Date
Practice 6-4
Special Parallelograms
For each parallelogram, (a) choose the best name, and then (b) find the measures of the numbered angles. 18
2.
3.
54 1
4
4
2 3
4.
1
4 106 3
3
1
5. 1
1
30
4
2 3 59
2
2
4
2
6.
3 60
1
2 3 4
68
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1.
The parallelograms below are not drawn to scale. Can the parallelogram have the conditions marked? If not, write impossible. Explain your answer.
7.
8.
9.
5 3.5 3.5 5
10. HJ = x and IK = 2x - 7
11. HJ = 3x + 5 and IK = 5x - 9
12. HJ = 3x + 7 and IK = 6x - 11
13. HJ = 19 + 2x and IK = 3x + 22
For each rhombus, (a) find the measures of the numbered angles, and then (b) find the area.
14.
15. AC = 8 in. BD = 22 in.
16 cm
29 9 cm
1 2 20
3 4 D
16.
A 1 2
52
B 1
10 m 2
4
3
13 m
3 4 C
Determine whether the quadrilateral can be a parallelogram. If not, write impossible. Explain your answer.
17. One pair of opposite sides is parallel, and the other pair is congruent. 18. Opposite angles are congruent and supplementary, but the quadrilateral is not a rectangle.
4
Lesson 6-4 Practice
Geometry Chapter 6
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HIJK is a rectangle. Find the value of x and the length of each diagonal.
Name
Class
Date
Practice 6-5
Trapezoids and Kites
Find the measures of the numbered angles in each isosceles trapezoid.
1.
2.
2
3.
99
62
1
1
1
4.
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2
5.
2
96
2
121
2
1
1
6.
2 1
67
G O
3 CS 060
79
Algebra Find the value(s) of the variable(s) in each isosceles trapezoid.
7.
(6x 20)
8.
3x 3
y x1
L
9.
M 2x 5
7x
(4x) x5
O
N
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Find the measures of the numbered angles in each kite.
10. 1
101
11.
12.
1 80
44
2
2
65
1
2
48
13.
14.
2 1
51
15. 59
27
3
1 1
3
2 2
87
Algebra Find the value(s) of the variable(s) in each kite.
16.
(5x 1)
17. (2x)° (10x 6)
18.
(y 9)
(4x 13)
(8x) (3x)
Geometry Chapter 6
(5x 15)
Lesson 6-5 Practice
y
5
Name
Class
Date
Practice 6-6
Placing Figures in the Coordinate Plane
Find the coordinates of the midpoint of each segment and find the length of each segment.
1. ME
y M (a, 2b)
E (2a, 2b)
2. ET 3. TR 4. RM
x
R (0, 0) T (a, 0)
y
5. DI
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Find the slope of each segment. E (a, 2a)
6. IR
R (3a, a)
7. RE
x
D (0, 0) I (2a, 0)
8. DE y N (2a, 4b)
9. VE 10. ER
I (6a, 4b)
E V
R
11. RB
B K (0, 0)
C (8a, 0) x
Use the properties of each figure to find the missing coordinates.
13. square
14. rectangle
y E (?, ?)
15. parallelogram y
S (3a, 2b)
R (4a, 3b)
y J (a, b)
O (3a, ?)
D (?, b)
x T (a, 0)
I (?, ?)
x
16. rhombus y
E (?, 2b)
(0, 0)
17. isosceles trapezoid y I (0, b)
L (0, 3a)
C (?, ?)
K (a, 0)
6
x
Lesson 6-6 Practice
H (3a, 0)
x
y
L (?, ?) x
I (3a, ?)
18. kite
A (?, 4b) R (?, b)
T (0, ?)
M (?, ?)
U (b, 0) x
C (a, 0) N (0, 4a)
Geometry Chapter 6
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12. VB
Name
Class
Date
All rights reserved.
Practice 6-7
Proofs Using Coordinate Geometry
1. Given HAL with perpendicular bisectors i, b, and m, complete the following to show that i, b, and m intersect in a point. 2q a. The slope of HA is p . What is the slope of line i? b. The midpoint of HA is (p, q). Show that the equation of line i is p p2 y = qx + q - q. c. The midpoint of HL is (r + p, 0). What is the equation of line m? rp d. Show that lines i and m intersect at (r + p, q + q). 2q e. The slope of AL is r . What is the slope of line b? f. What is the midpoint of AL? 2 g. Show that the equation of line b is y = qr x + q - rq . rp h. Show that lines b and m intersect at (r + p, q + q). i. Give the coordinates for the point of intersection of i, b, and m.
y A (0, 2q) b
i
H (2p, 0) L (2r, 0) x
m
Complete Exercises 2 and 3 without using any new variables.
2. RHCP is a rhombus. a. Determine the coordinates of R. b. Determine the coordinates of H. c. Find the midpoint of RH. d. Find the slope of RH.
y H C (0, 0) x
R
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P (a, b)
3. ADFS is a kite. a. Determine the coordinates of S. b. Find the midpoint of AS. c. Find the slope of AS. d. Find the midpoint of DF. e. Find the slope of DF.
4. Complete the coordinates for rectangle DHCP. Then use coordinate geometry to prove the following statement: The diagonals of a rectangle are congruent (Theorem 6-11).
y A (0, 6a)
S
D (4a, 0) x F (0, 2a)
y D
H (2a, 2b)
Given: rectangle DHCP Prove: DC HP
Geometry Chapter 6
P (0, 0)
Lesson 6-7 Practice
C
x
7
