Geometry Chapter 4 Worksheets d2yj
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MCRBG-0401-PA.qxd
4-19-2001
11:59 AM
Page 15
LESSON
NAME _________________________________________________________ DATE ___________
4.1
Practice A For use with pages 194–201
In the figure, AB BC and BD AC. Complete the sentence.
A
1. BC is the ______ of right triangle BDC. 2. BD is a ______ of right triangle BDC. 3. AC is the ______ of isosceles triangle ABC.
D
4. The legs of isosceles triangle ABC are ______ and ______.
B
C
Classify the triangle by its angles and by its sides. 6.
7.
8.
10.
11.
30
75
75
9.
115
108
Classify the sentence with always, sometimes, or never. 12. An equilateral triangle is ______ an isosceles triangle. 13. An isosceles triangle is ______ an equilateral triangle. 14. A right triangle is ______ an acute triangle. 15. An exterior angle of a triangle is ______ acute.
Find the measure of the numbered angle. 16.
17.
1
53
18. 1
42
33
2
68
2 102
1
Copyright © McDougal Littell Inc. All rights reserved.
Geometry Chapter 4 Resource Book
15
Lesson 4.1
5. The legs of right triangle ADB are ______ and ______.
MCRBG-0402-PA.qxd
4-19-2001
12:17 PM
Page 30
LESSON
4.2
NAME _________________________________________________________ DATE ___________
Practice A For use with pages 202–210
1. Given ABC DEF, name three
2. Given MNO PQR, name three
pairs of congruent sides.
pairs of congruent angles.
A
D
N
Q
M B
C
P
E
F
O
R
3. Copy the congruent triangles shown at the right.
Lesson 4.2
Then label the vertices of your triangles so that RUV TNF. Identify all pairs of congruent corresponding angles and corresponding sides.
In the diagram, MKL JET. Complete the statement. 4. L 6. mM
M
J
5. MK
6 cm 85
7. mT
8. ML
32
L
9. ETJ
K
T
E
Complete this statement. 10. If WRD PLK, then WR 12. If SVP MTQ, then PS
. .
14. If RHK WVO, then KRH
11. If BGT DSN, then T
.
13. If JCX MWP, then XC
.
. 15. If PMC LDX, then M
.
Identify any figures that can be proved congruent. Explain your reasoning. For those that can be proved congruent, write a congruence statement. 16. A
17.
B
X W
D
Y
C
18. M
Z
19.
I
O
H N
30
P
J
K
Q
Geometry Chapter 4 Resource Book
L
Copyright © McDougal Littell Inc. All rights reserved.
MCRBG-0403-PA.qxd
4-19-2001
12:52 PM
Page 45
LESSON
NAME _________________________________________________________ DATE ___________
4.3
Practice A For use with pages 212–219
Use the diagram. Name the included angle between the pair of sides given. 1. MT and TR
2. TQ and RT
3. RT and MR
4. TQ and RQ
5. MR and TM
6. RT and QR
M
T
R
Q
For each pair of congruent triangles, name the pairs of corresponding sides. 7. ABC TDF 8. DCT FLG 9. PWR ADE
Decide whether enough information is given to prove that the triangles are congruent. If there is enough information, state the congruence postulate you would use. 10. XYW, ZWY X
11. MAE, TAE Y
12. KHJ, KLJ L
E M
T
K W
Z
J
A
H
13. DKA, TKS
14. ENV, LOV E
A
15. TRA, GRA L
A
S
N
V
O T
T
R
G
Complete the proof by supplying the reasons. 16. Given: O is the midpoint of MQ.
O is the midpoint of NP. Prove: MON QOP M P O N Q
Copyright © McDougal Littell Inc. All rights reserved.
Statements
Reasons
1. O is the midpoint of MQ.
1.
?
2. MO QO
2.
?
3. O is the midpoint of NP.
3.
?
4. NO PO
4.
?
5. MON QOP
5.
?
6. MON QOP
6.
?
Geometry Chapter 4 Resource Book
45
Lesson 4.3
K D
MCRBG-0404-PA.qxd
4-30-2001
3:31 PM
Page 59
LESSON
NAME _________________________________________________________ DATE ___________
4.4
Practice A For use with pages 220–227
State the third congruence that must be given to prove that ABC DEF using the indicated postulate or theorem. 1. ASA Congruence Postulate F
2. AAS Congruence Theorem D
A
D
B
B E
E A
C
F
C
3. SSS Congruence Postulate B
4. SAS Congruence Postulate D
C
A
F
E
B E
C
D
F
A
Is it possible to prove that the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning. 5.
6.
W
C
7.
A
T
S
O
X
D
Z
Y
R F
Complete the proof by supplying the reasons.
L
8. Given: LA SN, LR NR
Prove: LAR NSR S L R
Reasons
1. LA SN
1.
?
2. L N
2.
?
3. LR NR
3.
?
4. LRA NRS
4.
?
5. LAR NSR
5.
?
Write a two-column or a paragraph proof.
A
Lesson 4.4
N A
Statements
B
9. Given: AB CD, AC BD
Prove: ABC DCB C Copyright © McDougal Littell Inc. All rights reserved.
D Geometry Chapter 4 Resource Book
59
MCRBG-0405-PA.qxd
4-19-2001
2:06 PM
Page 72
Lesson 4.5
LESSON
4.5
NAME _________________________________________________________ DATE ___________
Practice A For use with pages 229–235
Use the diagram to answer the following.
I
1. What triangles appear to be congruent? 2. To prove IKS EKS, which triangles must you
prove to be congruent?
S
K
T
3. To prove TIS TES, which triangles must you
prove to be congruent? 4. To prove IK EK, which triangles must you prove E
to be congruent? Use the diagram to answer the following.
P
5. If PDA RDL, then 1 corresponds to
?
.
6. If PRA RPL, then 1 corresponds to
?
.
A 3 1
2 7
7. If PDL RDA, then name 3 pair of corresponding angles.
4 8 9
D
6
8. If PDL RDA, then name 3 pair of corresponding sides.
11
12
L
5
10 R
Use the marked diagram to state the method used to prove the triangles congruent. Name the additional corresponding parts that could then be concluded to be congruent. 9.
10. B
A T
11.
W
X
N M O C
X M
N C Z
Y
Complete the proof by supplying the reasons. 12. Given: AB DC, AD BC
Prove: A C A
D
B
C
Write a two-column or a paragraph proof.
Statements
Reasons
1. AB DC
1.
?
2. AD BC
2.
?
3. BD BD
3.
?
4. ABD CDB 4.
?
5. A C
?
5.
A E
13. Given: AC DC, A D
C
Prove: B E B D 72
Geometry Chapter 4 Resource Book
Copyright © McDougal Littell Inc. All rights reserved.
MCRBG-0406-PA.qxd
4-19-2001
2:28 PM
Page 85
LESSON
NAME _________________________________________________________ DATE ___________
4.6
Practice A For use with pages 236–242 R
Use the diagram to answer the following.
1
1. If RI IT, what angles are congruent? 2. If TN IT, what angles are congruent? 3. If 1 6, what segments are congruent?
2
I
4. The legs of isosceles triangle TNH are ______ and ______.
T
3
11 10
4
5
9 G
8
7 N
Lesson 4.6
5. The vertex angle of RGH is ______. 6 H
Solve for x and y. 6.
7.
8.
y
x x
x
y
y
72
Decide whether enough information is given to prove that the triangles are congruent. Explain your answer. 9.
10.
A
11.
N
M
B
O
U
R
T
O
C
D
P
S
Solve for x. 12.
13.
(3x 8)
(4x 10)
14. 54 x
40 (2x 20)
A
Write a two-column or a paragraph proof. 15. Given: BD bisects ADC.
DB AC
D
1 2
3 B 4
Prove: ADC is isosceles C Copyright © McDougal Littell Inc. All rights reserved.
Geometry Chapter 4 Resource Book
85
MCRBG-0407-PA.qxd
4-19-2001
2:53 PM
Page 102
LESSON
NAME _________________________________________________________ DATE ___________
4.7
Practice A For use with pages 243–250
Find the missing coordinates. 1.
2.
y
3.
y
B(—, —)
B(—, —)
y
A(5, 3)
A(3, 4) D(—, —) x
1
A(8, 0)
x
B(2, 4)
x
C(—, —)
D(—, —) C(—, —)
Find the missing coordinates without using any new variables. 4.
5.
y
6.
y
B(—, —) y
B(0, b) A(a, b)
B(—, —)
A(a, 0) x
Lesson 4.7
C(—, —) C(—, —) x
A(a, 0) x
C(—, —)
D(—, —)
Place the figure in the coordinate plane. Label the vertices and give the coordinates of each vertex. 7. An isosceles right triangle with legs of 12 units 8. A rectangle with a length of 16 units and a width of 8 units 9. A square with a perimeter of 36 units
Place the figure in the coordinate plane and find the given information. 10. A right triangle with legs of 8 and 10 units; find the length of the hypotenuse. 11. A rectangle with a length of 20 units and a width of 12 units; find the
length of a diagonal. 12. A square with an area of 25 square units; find the length of a diagonal.
Write a paragraph proof.
y
13. Given: OM LN
L(0, 12)
Prove: OM bisects LON.
M 2 2
102
Geometry Chapter 4 Resource Book
O(0, 0)
N(12, 0) x
Copyright © McDougal Littell Inc. All rights reserved.
4-19-2001
11:59 AM
Page 15
LESSON
NAME _________________________________________________________ DATE ___________
4.1
Practice A For use with pages 194–201
In the figure, AB BC and BD AC. Complete the sentence.
A
1. BC is the ______ of right triangle BDC. 2. BD is a ______ of right triangle BDC. 3. AC is the ______ of isosceles triangle ABC.
D
4. The legs of isosceles triangle ABC are ______ and ______.
B
C
Classify the triangle by its angles and by its sides. 6.
7.
8.
10.
11.
30
75
75
9.
115
108
Classify the sentence with always, sometimes, or never. 12. An equilateral triangle is ______ an isosceles triangle. 13. An isosceles triangle is ______ an equilateral triangle. 14. A right triangle is ______ an acute triangle. 15. An exterior angle of a triangle is ______ acute.
Find the measure of the numbered angle. 16.
17.
1
53
18. 1
42
33
2
68
2 102
1
Copyright © McDougal Littell Inc. All rights reserved.
Geometry Chapter 4 Resource Book
15
Lesson 4.1
5. The legs of right triangle ADB are ______ and ______.
MCRBG-0402-PA.qxd
4-19-2001
12:17 PM
Page 30
LESSON
4.2
NAME _________________________________________________________ DATE ___________
Practice A For use with pages 202–210
1. Given ABC DEF, name three
2. Given MNO PQR, name three
pairs of congruent sides.
pairs of congruent angles.
A
D
N
Q
M B
C
P
E
F
O
R
3. Copy the congruent triangles shown at the right.
Lesson 4.2
Then label the vertices of your triangles so that RUV TNF. Identify all pairs of congruent corresponding angles and corresponding sides.
In the diagram, MKL JET. Complete the statement. 4. L 6. mM
M
J
5. MK
6 cm 85
7. mT
8. ML
32
L
9. ETJ
K
T
E
Complete this statement. 10. If WRD PLK, then WR 12. If SVP MTQ, then PS
. .
14. If RHK WVO, then KRH
11. If BGT DSN, then T
.
13. If JCX MWP, then XC
.
. 15. If PMC LDX, then M
.
Identify any figures that can be proved congruent. Explain your reasoning. For those that can be proved congruent, write a congruence statement. 16. A
17.
B
X W
D
Y
C
18. M
Z
19.
I
O
H N
30
P
J
K
Q
Geometry Chapter 4 Resource Book
L
Copyright © McDougal Littell Inc. All rights reserved.
MCRBG-0403-PA.qxd
4-19-2001
12:52 PM
Page 45
LESSON
NAME _________________________________________________________ DATE ___________
4.3
Practice A For use with pages 212–219
Use the diagram. Name the included angle between the pair of sides given. 1. MT and TR
2. TQ and RT
3. RT and MR
4. TQ and RQ
5. MR and TM
6. RT and QR
M
T
R
Q
For each pair of congruent triangles, name the pairs of corresponding sides. 7. ABC TDF 8. DCT FLG 9. PWR ADE
Decide whether enough information is given to prove that the triangles are congruent. If there is enough information, state the congruence postulate you would use. 10. XYW, ZWY X
11. MAE, TAE Y
12. KHJ, KLJ L
E M
T
K W
Z
J
A
H
13. DKA, TKS
14. ENV, LOV E
A
15. TRA, GRA L
A
S
N
V
O T
T
R
G
Complete the proof by supplying the reasons. 16. Given: O is the midpoint of MQ.
O is the midpoint of NP. Prove: MON QOP M P O N Q
Copyright © McDougal Littell Inc. All rights reserved.
Statements
Reasons
1. O is the midpoint of MQ.
1.
?
2. MO QO
2.
?
3. O is the midpoint of NP.
3.
?
4. NO PO
4.
?
5. MON QOP
5.
?
6. MON QOP
6.
?
Geometry Chapter 4 Resource Book
45
Lesson 4.3
K D
MCRBG-0404-PA.qxd
4-30-2001
3:31 PM
Page 59
LESSON
NAME _________________________________________________________ DATE ___________
4.4
Practice A For use with pages 220–227
State the third congruence that must be given to prove that ABC DEF using the indicated postulate or theorem. 1. ASA Congruence Postulate F
2. AAS Congruence Theorem D
A
D
B
B E
E A
C
F
C
3. SSS Congruence Postulate B
4. SAS Congruence Postulate D
C
A
F
E
B E
C
D
F
A
Is it possible to prove that the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning. 5.
6.
W
C
7.
A
T
S
O
X
D
Z
Y
R F
Complete the proof by supplying the reasons.
L
8. Given: LA SN, LR NR
Prove: LAR NSR S L R
Reasons
1. LA SN
1.
?
2. L N
2.
?
3. LR NR
3.
?
4. LRA NRS
4.
?
5. LAR NSR
5.
?
Write a two-column or a paragraph proof.
A
Lesson 4.4
N A
Statements
B
9. Given: AB CD, AC BD
Prove: ABC DCB C Copyright © McDougal Littell Inc. All rights reserved.
D Geometry Chapter 4 Resource Book
59
MCRBG-0405-PA.qxd
4-19-2001
2:06 PM
Page 72
Lesson 4.5
LESSON
4.5
NAME _________________________________________________________ DATE ___________
Practice A For use with pages 229–235
Use the diagram to answer the following.
I
1. What triangles appear to be congruent? 2. To prove IKS EKS, which triangles must you
prove to be congruent?
S
K
T
3. To prove TIS TES, which triangles must you
prove to be congruent? 4. To prove IK EK, which triangles must you prove E
to be congruent? Use the diagram to answer the following.
P
5. If PDA RDL, then 1 corresponds to
?
.
6. If PRA RPL, then 1 corresponds to
?
.
A 3 1
2 7
7. If PDL RDA, then name 3 pair of corresponding angles.
4 8 9
D
6
8. If PDL RDA, then name 3 pair of corresponding sides.
11
12
L
5
10 R
Use the marked diagram to state the method used to prove the triangles congruent. Name the additional corresponding parts that could then be concluded to be congruent. 9.
10. B
A T
11.
W
X
N M O C
X M
N C Z
Y
Complete the proof by supplying the reasons. 12. Given: AB DC, AD BC
Prove: A C A
D
B
C
Write a two-column or a paragraph proof.
Statements
Reasons
1. AB DC
1.
?
2. AD BC
2.
?
3. BD BD
3.
?
4. ABD CDB 4.
?
5. A C
?
5.
A E
13. Given: AC DC, A D
C
Prove: B E B D 72
Geometry Chapter 4 Resource Book
Copyright © McDougal Littell Inc. All rights reserved.
MCRBG-0406-PA.qxd
4-19-2001
2:28 PM
Page 85
LESSON
NAME _________________________________________________________ DATE ___________
4.6
Practice A For use with pages 236–242 R
Use the diagram to answer the following.
1
1. If RI IT, what angles are congruent? 2. If TN IT, what angles are congruent? 3. If 1 6, what segments are congruent?
2
I
4. The legs of isosceles triangle TNH are ______ and ______.
T
3
11 10
4
5
9 G
8
7 N
Lesson 4.6
5. The vertex angle of RGH is ______. 6 H
Solve for x and y. 6.
7.
8.
y
x x
x
y
y
72
Decide whether enough information is given to prove that the triangles are congruent. Explain your answer. 9.
10.
A
11.
N
M
B
O
U
R
T
O
C
D
P
S
Solve for x. 12.
13.
(3x 8)
(4x 10)
14. 54 x
40 (2x 20)
A
Write a two-column or a paragraph proof. 15. Given: BD bisects ADC.
DB AC
D
1 2
3 B 4
Prove: ADC is isosceles C Copyright © McDougal Littell Inc. All rights reserved.
Geometry Chapter 4 Resource Book
85
MCRBG-0407-PA.qxd
4-19-2001
2:53 PM
Page 102
LESSON
NAME _________________________________________________________ DATE ___________
4.7
Practice A For use with pages 243–250
Find the missing coordinates. 1.
2.
y
3.
y
B(—, —)
B(—, —)
y
A(5, 3)
A(3, 4) D(—, —) x
1
A(8, 0)
x
B(2, 4)
x
C(—, —)
D(—, —) C(—, —)
Find the missing coordinates without using any new variables. 4.
5.
y
6.
y
B(—, —) y
B(0, b) A(a, b)
B(—, —)
A(a, 0) x
Lesson 4.7
C(—, —) C(—, —) x
A(a, 0) x
C(—, —)
D(—, —)
Place the figure in the coordinate plane. Label the vertices and give the coordinates of each vertex. 7. An isosceles right triangle with legs of 12 units 8. A rectangle with a length of 16 units and a width of 8 units 9. A square with a perimeter of 36 units
Place the figure in the coordinate plane and find the given information. 10. A right triangle with legs of 8 and 10 units; find the length of the hypotenuse. 11. A rectangle with a length of 20 units and a width of 12 units; find the
length of a diagonal. 12. A square with an area of 25 square units; find the length of a diagonal.
Write a paragraph proof.
y
13. Given: OM LN
L(0, 12)
Prove: OM bisects LON.
M 2 2
102
Geometry Chapter 4 Resource Book
O(0, 0)
N(12, 0) x
Copyright © McDougal Littell Inc. All rights reserved.
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