chapter 4 review - mr. lahaie's...
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Chapter 4 ReviewGeometry C
Classify each triangle by angles (acute, obtuse, right, equiangular) & by the sides (scalene, isosceles, equilateral).
1. ________________! 2. ________________! 3. ________________
________________ ________________ ________________
Find the missing angle of each triangle.
4.! m∠C = _________! ! ! ! 5.! x = _______! 2x = ________
! ! ! ! ! ! ! ! 3x = _______ 4x = ________
6.! ∆HAM ≅ ∆PIX. List all 6 pairs of congruent parts.!! _________________! _________________! _________________
! _________________! _________________! _________________
7.! ∆KLM ≅ ∆RST. Find the value of x.
! x = _________
Name: ________________________________________ Date: _________________ Hour: ________
Copyright © by Holt, Rinehart and Winston. 67 Holt GeometryAll rights reserved.
Name Date Class
CHAPTER
Circle the best answer.
1. What type of triangle is !ABC ?
30° 120°
30°
A acuteB equiangularC obtuseD right
2. How many sides must be congruent in an isosceles triangle?A at least 2B all 3
3. Which pair of angle measures CANNOT be the acute angles of a right triangle?A 29! and 61!
B 30! and 60!
C 38! and 53!
D 45! and 45!
4. What is m"ACD?
80°
50°
A 100B 130
5. Given: !TUV ! !TWV. What is the value of x ?
3 15
75
A 20B 123
6. If !KLM ! !RST, find the value of x.
A 18B 45
7. Given: "A ! "D, "B ! "E, "C ! "F,
_ AB !
_ DE , _
BC ! _
EF , and
_ CA !
_ FD . Which is a correct
congruence statement?A !BCA ! !DEFB !ABC ! !DEF
Use the figure for Exercises 8 and 9.
8. Which value for x proves that !ABC ! !DEF by SSS?A 7B 37
9. What additional information would allow you to prove the triangles congruent by SAS?A "E ! "DB "D ! "CC "D ! "AD "F ! "C
Chapter TestForm A4
Copyright © by Holt, Rinehart and Winston. 69 Holt GeometryAll rights reserved.
Name Date Class
Chapter TestForm B
CHAPTER
Circle the best answer.
1. Classify the triangle.
60°85°
35°
A isosceles acute C scalene acuteB isosceles obtuse D scalene obtuse
Use the figure for Exercises 2 and 3.
60° 60°
60°3 1 5
2. Which is NOT a correct classification for the triangle?F acute H isoscelesG equiangular J scalene
3. What is the length of side _
BC ?A 3 C 10B 8 D 24
Use the figure for Exercises 4 and 5.
(8 18)°
(6 4)°
(20 4)°
4. What is m!KLM?F 3 H 42G 22 J 64
5. What is m!M?A 0.2 C 26B 4 D 64
6. What is the m!U?
F 5 H 40G 15 J 120
7. Two congruent triangles have the following corresponding parts: _
RS ! _
UV , _
RT ! _
UW , and !R ! !U. Which is NOT necessarily a correct congruence statement?A "RST ! "UVWB "STR ! "VWUC "TRS ! "VWUD "TRS ! "WUV
8. "KLM ! "RST. m!L ! (3x " 15)# and m!S ! (6x " 3)#. What is the value of x?F 2 H 6G 4 J 27
Use the figure for Exercises 9 –12.
9. If AD ! 5y " 7 and BC ! 7y $ 3, what must the value of y be to prove "AED ! "CEB by the SSS Postulate?A 2 C 17B 5 D 32
10. What postulate or theorem justifies the congruence statement "ABE ! "CDE?F SSS H ASAG SAS J AAS
4
Copyright © by Holt, Rinehart and Winston. 68 Holt GeometryAll rights reserved.
Name Date Class
CHAPTER
Use the figure for Exercises 10 and 11.
10. Which postulate or theorem can you use to prove !ABE and !CDE ?A SSSB SASC ASAD AAS
11. What additional information will prove !ABE ! !CDE by HL?A _
AB ! _
CD B _
AE ! _
CE
12. To write a coordinate proof, you position a right isosceles triangle in the coordinate plane. The legs measure two units. What is the best position for the vertex angle?A (0,0)B (0,2)C (2, 0)D (2, 2)
13. Given: ABCD is a square with vertices A (0,0), B(0, 4), C (4, 4), and D (4,0). In a coordinate proof, what information would be used to prove
_ AB !
_ CD if you do
NOT use the distance formula?A x-coordinate of A, x-coordinate of CB y-coordinate of A, y-coordinate of CC y-coordinate of A, x-coordinate of CD x-coordinate of A, y-coordinate of C
14. What is the value of x?
A 22.5B 30C 45D 60
Use the figure for Exercises 15 and 16.
15. What postulate or theorem proves _
HG ! _
FG ?A Isosceles Triangle TheoremB Converse of Isosceles Triangle
Theorem
16. If !FGJ ! !HGJ, what reason justifies the statement "HGJ ! "FGJ?A ASAB Reflex. Prop. of !C Def. of bisectsD CPCTC
Chapter TestForm A continued4
Copyright © by Holt, Rinehart and Winston. 67 Holt GeometryAll rights reserved.
Name Date Class
CHAPTER
Circle the best answer.
1. What type of triangle is !ABC ?
30° 120°
30°
A acuteB equiangularC obtuseD right
2. How many sides must be congruent in an isosceles triangle?A at least 2B all 3
3. Which pair of angle measures CANNOT be the acute angles of a right triangle?A 29! and 61!
B 30! and 60!
C 38! and 53!
D 45! and 45!
4. What is m"ACD?
80°
50°
A 100B 130
5. Given: !TUV ! !TWV. What is the value of x ?
3 15
75
A 20B 123
6. If !KLM ! !RST, find the value of x.
A 18B 45
7. Given: "A ! "D, "B ! "E, "C ! "F,
_ AB !
_ DE , _
BC ! _
EF , and
_ CA !
_ FD . Which is a correct
congruence statement?A !BCA ! !DEFB !ABC ! !DEF
Use the figure for Exercises 8 and 9.
8. Which value for x proves that !ABC ! !DEF by SSS?A 7B 37
9. What additional information would allow you to prove the triangles congruent by SAS?A "E ! "DB "D ! "CC "D ! "AD "F ! "C
Chapter TestForm A4
2x
3x
4x
Copyright © by Holt, Rinehart and Winston. 67 Holt GeometryAll rights reserved.
Name Date Class
CHAPTER
Circle the best answer.
1. What type of triangle is !ABC ?
30° 120°
30°
A acuteB equiangularC obtuseD right
2. How many sides must be congruent in an isosceles triangle?A at least 2B all 3
3. Which pair of angle measures CANNOT be the acute angles of a right triangle?A 29! and 61!
B 30! and 60!
C 38! and 53!
D 45! and 45!
4. What is m"ACD?
80°
50°
A 100B 130
5. Given: !TUV ! !TWV. What is the value of x ?
3 15
75
A 20B 123
6. If !KLM ! !RST, find the value of x.
A 18B 45
7. Given: "A ! "D, "B ! "E, "C ! "F,
_ AB !
_ DE , _
BC ! _
EF , and
_ CA !
_ FD . Which is a correct
congruence statement?A !BCA ! !DEFB !ABC ! !DEF
Use the figure for Exercises 8 and 9.
8. Which value for x proves that !ABC ! !DEF by SSS?A 7B 37
9. What additional information would allow you to prove the triangles congruent by SAS?A "E ! "DB "D ! "CC "D ! "AD "F ! "C
Chapter TestForm A4
8.! ∆TUV ≅ ∆TWV. Find the value of x.
! x = _________
Identify which triangle congruence theorem will prove these triangles congruent. (SSS, SAS, ASA, AAS, or none)
9.! ! ! ! 10.! ! ! ! 11.
12.! ! ! ! 13.! ! ! ! 14.
15.! ! ! ! 16.! ! ! ! 17.
18.! ! ! ! 19.! ! ! ! 120.
Name: ________________________________________ Date: _________________ Hour: ________
Copyright © by Holt, Rinehart and Winston. 69 Holt GeometryAll rights reserved.
Name Date Class
Chapter TestForm B
CHAPTER
Circle the best answer.
1. Classify the triangle.
60°85°
35°
A isosceles acute C scalene acuteB isosceles obtuse D scalene obtuse
Use the figure for Exercises 2 and 3.
60° 60°
60°3 1 5
2. Which is NOT a correct classification for the triangle?F acute H isoscelesG equiangular J scalene
3. What is the length of side _
BC ?A 3 C 10B 8 D 24
Use the figure for Exercises 4 and 5.
(8 18)°
(6 4)°
(20 4)°
4. What is m!KLM?F 3 H 42G 22 J 64
5. What is m!M?A 0.2 C 26B 4 D 64
6. What is the m!U?
F 5 H 40G 15 J 120
7. Two congruent triangles have the following corresponding parts: _
RS ! _
UV , _
RT ! _
UW , and !R ! !U. Which is NOT necessarily a correct congruence statement?A "RST ! "UVWB "STR ! "VWUC "TRS ! "VWUD "TRS ! "WUV
8. "KLM ! "RST. m!L ! (3x " 15)# and m!S ! (6x " 3)#. What is the value of x?F 2 H 6G 4 J 27
Use the figure for Exercises 9 –12.
9. If AD ! 5y " 7 and BC ! 7y $ 3, what must the value of y be to prove "AED ! "CEB by the SSS Postulate?A 2 C 17B 5 D 32
10. What postulate or theorem justifies the congruence statement "ABE ! "CDE?F SSS H ASAG SAS J AAS
4
21.! ∆ABC ≅ ∆DEF. Find the value of x.
! x = _________
22.! Use the figure below. Find the value of x.
! x = _________
23.! Use the figure below. Find the angles below.!
! a.! ∠A = _________
! b.! ∠B = _________
24.! Use the figure below. Find the angles below.!
! a.! ∠X = _________
! b.! ∠Z = _________
25.! Find the measure of each angle using the diagram below.
! ∠J = _________!
! ∠K = _________
! ∠L = _________
Name: ________________________________________ Date: _________________ Hour: ________
Copyright © by Holt, Rinehart and Winston. 67 Holt GeometryAll rights reserved.
Name Date Class
CHAPTER
Circle the best answer.
1. What type of triangle is !ABC ?
30° 120°
30°
A acuteB equiangularC obtuseD right
2. How many sides must be congruent in an isosceles triangle?A at least 2B all 3
3. Which pair of angle measures CANNOT be the acute angles of a right triangle?A 29! and 61!
B 30! and 60!
C 38! and 53!
D 45! and 45!
4. What is m"ACD?
80°
50°
A 100B 130
5. Given: !TUV ! !TWV. What is the value of x ?
3 15
75
A 20B 123
6. If !KLM ! !RST, find the value of x.
A 18B 45
7. Given: "A ! "D, "B ! "E, "C ! "F,
_ AB !
_ DE , _
BC ! _
EF , and
_ CA !
_ FD . Which is a correct
congruence statement?A !BCA ! !DEFB !ABC ! !DEF
Use the figure for Exercises 8 and 9.
8. Which value for x proves that !ABC ! !DEF by SSS?A 7B 37
9. What additional information would allow you to prove the triangles congruent by SAS?A "E ! "DB "D ! "CC "D ! "AD "F ! "C
Chapter TestForm A4
Copyright © by Holt, Rinehart and Winston. 68 Holt GeometryAll rights reserved.
Name Date Class
CHAPTER
Use the figure for Exercises 10 and 11.
10. Which postulate or theorem can you use to prove !ABE and !CDE ?A SSSB SASC ASAD AAS
11. What additional information will prove !ABE ! !CDE by HL?A _
AB ! _
CD B _
AE ! _
CE
12. To write a coordinate proof, you position a right isosceles triangle in the coordinate plane. The legs measure two units. What is the best position for the vertex angle?A (0,0)B (0,2)C (2, 0)D (2, 2)
13. Given: ABCD is a square with vertices A (0,0), B (0, 4), C (4, 4), and D (4,0). In a coordinate proof, what information would be used to prove
_ AB !
_ CD if you do
NOT use the distance formula?A x-coordinate of A, x-coordinate of CB y-coordinate of A, y-coordinate of CC y-coordinate of A, x-coordinate of CD x-coordinate of A, y-coordinate of C
14. What is the value of x?
A 22.5B 30C 45D 60
Use the figure for Exercises 15 and 16.
15. What postulate or theorem proves _
HG ! _
FG ?A Isosceles Triangle TheoremB Converse of Isosceles Triangle
Theorem
16. If !FGJ ! !HGJ, what reason justifies the statement "HGJ ! "FGJ?A ASAB Reflex. Prop. of !C Def. of bisectsD CPCTC
Chapter TestForm A continued4
44º
A
B
C
X
Y Z35º
Copyright © by Holt, Rinehart and Winston. 68 Holt GeometryAll rights reserved.
Name Date Class
CHAPTER
Use the figure for Exercises 10 and 11.
10. Which postulate or theorem can you use to prove !ABE and !CDE ?A SSSB SASC ASAD AAS
11. What additional information will prove !ABE ! !CDE by HL?A _
AB ! _
CD B _
AE ! _
CE
12. To write a coordinate proof, you position a right isosceles triangle in the coordinate plane. The legs measure two units. What is the best position for the vertex angle?A (0,0)B (0,2)C (2, 0)D (2, 2)
13. Given: ABCD is a square with vertices A (0,0), B(0, 4), C (4, 4), and D (4,0). In a coordinate proof, what information would be used to prove
_ AB !
_ CD if you do
NOT use the distance formula?A x-coordinate of A, x-coordinate of CB y-coordinate of A, y-coordinate of CC y-coordinate of A, x-coordinate of CD x-coordinate of A, y-coordinate of C
14. What is the value of x?
A 22.5B 30C 45D 60
Use the figure for Exercises 15 and 16.
15. What postulate or theorem proves _
HG ! _
FG ?A Isosceles Triangle TheoremB Converse of Isosceles Triangle
Theorem
16. If !FGJ ! !HGJ, what reason justifies the statement "HGJ ! "FGJ?A ASAB Reflex. Prop. of !C Def. of bisectsD CPCTC
Chapter TestForm A continued4
J
K
L