1. No category

Test 1 Review
Name: _______________________
1. Which triangle congruence criteria will determine congruence for
given diagram?
A) SSS
B) SAS
C) ASA
D) AAS
E) HL
B
E
B) AB ≅ ED
C) C is the midpoint of AE
D) ∠A ≅ ∠E
1. ________
C
A
D
E
2. Three of the four items listed can be used to establish congruence by ASA.
Determine which one is NOT needed to prove ∆BCA ≅ ∆DCE by ASA?
A) ∠DCE AND ∠BCA are vertical ∠’s
1
B
2. ________
C
D
A
3. ∆ABC has m∠C = 42° and m∠A = 80°, then the correct classification for the triangle is:
A) Acute
B) Right
C) Obtuse
D) Isosceles
3. ________
4. If isosceles ∆ABC has a base angle, ∠B, with a measure of 45°, then ∆ABC is
A) an acute ∆
B) a right ∆
C) an obtuse ∆
D) a scalene ∆
4. ________
5. Which of the following is NOT a characteristic of all parallelograms?
A) Diagonal bisect each other
congruent
C) Diagonals are angle bisectors
B) Opposite angles are
5. ________
D) Opposite sides are congruent
6. Which of the following is NOT a characteristic of all rectangles?
A) Consecutive angles are supplementary
congruent
C) Diagonals bisect each other
B) Opposite angles are
6. ________
D) Diagonals are perpendicular
7. Which of the following is NOT a characteristic of all rhombi?
A) Four congruent sides
B) Diagonals are angle bisectors
C) Diagonals are perpendicular
D) Diagonals are congruent
7. ________
8. Which of the following group of quadrilaterals have diagonals that are perpendicular?
A) Rhombus, Square
B) Rhombus, Parallelogram, Square
C) Rectangle, Square
D) Rectangle, Rhombus, Square
9. What is the value of the function, f ( x) = 3x − 1 when x = -3?
A) 8
B) - 10
C) -8
9. _____
D) - 1
x
, what is the value of x when f ( x) = 16 ?
4
B) x = -4
C) x = 64
D) x = 8
10. Given the function, f ( x) =
A) x = 4
8. ________
11. A student places x = 3 into the function, f ( x) = 5 x − 7 and gets f ( x) = 8 . f ( x) = 8 is
the:
A) Input
B) Output
C) Domain
D) Maximum
10. _____
11. _____
Test 1 Review
2
12. Which diagram is a NOT a One to One Function?
12. _____
A)
B)
C)
D)
13. Which diagram is not transformation?
Pre-Image
Pre-Image
Image
Pre-Image
Image
Pre-Image
Image
Image
13. _____
A)
B)
C)
D)
14. If you have a rotational symmetry angle of 18°, then your order is:
A) 2
B) 5
C) 10
15. Which of the following has exactly one line of symmetry?
A) A Rectangle B) An Isosceles Trapezoid C) A Rhombus
D) 20
14. _____
D) A Parallelogram
15. _____
16. This shape has:
A) Only Rotational Symmetry B) Only Reflectional Symmetry
16. _____
C) Both Rotational & Reflectional Symmetries D) Neither symmetry
17. ∆ABC is reflected to create image ∆A’B’C’. Which statement is always true?
A) AB || A ' B '
B) AA ' ⊥ BB '
C) AB ⊥ A ' B '
D) AA ' || BB '
17. _____
18. AB is rotated 87° about point T. Which of the following statements is false?
A) T = T’
B) AT = A’T
C) AA’ = BB’
D) m∠ATA’ = 87°
18. _____
19. Which transformation changes the orientation of the shape?
A) Rotation
B) Dilation
C) Translation
D) Reflection
19. _____
20. If RO ,167° ( ∆ABC ) = ∆DEF then:
A) m∠BOD = 167°
B) m∠OAD = 167°
C) m∠AOE = 167°
D) m∠FOC = 167°
20. _____
21. CPCFC stands for:
A) Congruent Parts of Congruent Figures are Congruent
B) Corresponding Parts of Congruent Figures are Congruent
C) Corresponding Parts of Corresponding Figures are Congruent
D) None of these
21. _____
22. If two triangles are congruent, then:
22. _____
A) they have the same side lengths B) isometric transformation(s) map one onto the other
C) they have the same angle
D) all of the above are true
Test 1 Review
3
23. A reflection maps these two quadrilaterals onto each other, thus they are congruent.
Which congruence statement represents this relationship?
A
F
I
D
23. _____
A) Quad ABCD ≅ Quad FGHI B) Quad DBCA ≅ Quad IFGH
C) Quad BCAD ≅ Quad HGIF
D) Quad CBDA ≅ Quad GHIF
B
H
C
G
m
24. A student believes that he can prove these two triangles to be congruent using SSS
24. _____
because he knows that BD ≅ BD . What would be his reason for knowing this?
C
A) The triangles are congruent
B) The Reflexive Property
D
B
C) It can’t be SAS because no angle is given D) The Substitution Property
E
25. _____
25. In ∆ABC, the included angle of AB and BC is:
A) ∠A
B) ∠B
C) ∠C D) unable to determine without diagram
26. To be able to prove that ∆ABD ≅ ∆CBD by HL, using the two given congruent
corresponding sides, one piece of information is missing. Which of the following
B
would be that piece of information?
A) Base angles of an isosceles are congruent
B) BD ≅ BD
C) BD bisect ∠ABC
D) ∠ADB is a right angle
26. _____
C
27. Three of the four items listed can be used to establish congruence
by ASA. Determine which one is NOT needed to prove ∆ABC ≅
∆EBD by ASA?
B) B is the midpoint of AE
A) ∠D ≅ ∠C
C) ∠E ≅ ∠A
D
A
D
27. _____
E
B
A
C
D) ∠DBE AND ∠CBA are vertical ∠’s
28. Three of the four items listed can be used to establish congruence by
SSS. Determine which one is NOT needed to prove ∆BCA ≅ ∆DCE by
SSS?
28. _____
E
B
C
A) AE is a common side
B) AB ≅ ED
C) C is the midpoint of AE
D) C is the midpoint of BD
D
A
Test 1 Review
4
B
29. Which triangle congruence criteria will determine congruence
for given diagram?
E
C
A) SSS
B) SAS
C) ASA
D) AAS
E) HL
30. Three of the four items listed can be used to establish
congruence by SAS. Determine which one is NOT needed to
prove ∆BCD ≅ ∆DEB by SAS?
A) BD ≅ BD
B) BC ≅ DE
C) ∠E ≅ ∠C
D) ∠CBD ≅ ∠EDB
A
D
29. _____
30. ____
C
D
B
E
31. Quadrilateral FHJK is congruent Quadrilateral MNPO. Complete the following congruent statements.
a) ∠J ≅ ∠ ______
b) NP ≅ ______
c) ∠M ≅ ∠ ______
d) KF ≅ ______
Determine whether the following are (T)rue or (F)alse.
32. ∆ABC has m∠A = 16° and m∠C = 57°, then the triangle is an obtuse triangle.
T or F
33. ∆ABC has m∠C = 71° and m∠B = 71°, then AB ≅ AC .
34. If isosceles ∆ABC has a vertex angle, ∠B, of 83°, then m∠A = 49°
35 A rhombus has four congruent angles.
36. A rectangle has diagonals that bisect each other.
37. Consecutive sides are congruent in a rectangle.
38. If a parallelogram has 4 ≅ angles, then it must be a square.
T
T
T
T
T
T
39. T ( x, y ) − − − − > ( x + 5, − y ) is an isometric transformation.
T or F
40. T ( x, y ) − − − − > (3x, y + 2) is an isometric transformation.
T or F
41. If a shape has a rotational order of 1, then it has NO rotational symmetry.
42. A rotational symmetry of order 2 means that the angle of the order is 90°.
43. If point A is 2.5 cm from the line of reflection, then AA’ = 5 cm.
44. A rotation of 180° reverses the orientation of the shape.
45. When a rotation of 80° about point T is performed, all points in the plane move.
46. The isometric transformations are rotation, reflection, dilation and translation.
47. Given ∆ABC & ∆RTS and ∠A ≅ ∠R, ∠B ≅ ∠T, ∠C ≅ ∠S then ∆ABC ≅ ∆RTS.
T
T
T
T
T
T
T
or
or
or
or
or
or
or
F
F
F
F
F
F
F
48. Given ∆ABC & ∆RTS and ∠A ≅ ∠R, BC ≅ TS , ∠C ≅ ∠S then ∆ABC ≅ ∆RTS.
49. If a translation maps A (-3,5) to A’ (3, 5), then T(x,y) ------> (x – 6,y) would be the rule.
50. F (x,y) -------> (x + 3,y) is a translation of 3 units to the right.
51. A rotation of 270°about the origin maps A (1,-2) to A’ (-2,-1)
52. RO ,180 = Rx axis Ry axis
T
T
T
T
T
or
or
or
or
or
F
F
F
F
F
53. Three reflections over parallel lines could also be described as a single translation.
T or F
or
or
or
or
or
or
F
F
F
F
F
F
Test 1 Review
5
54. A composite transformation of a rotation followed by translation reverses the
orientation of the shape.
55. A translation of 2 right and 5 down followed by a reflection on the x axis is T< 2,−5> Rx axis
T or F
T or F
56. A double reflection over y = 3 followed by y = 4, translates all points up 2 units.
57. A double reflection over y = -3 followed by y = -1, translates all points up 4 units.
58. Ry = 11 Ry = 6 = T<0,10 >
T or F
T or F
T or F
59. Determine the following for any point P.
k
a) R_________ R_________ ( P) would result in a rotation of 82°.
b) R_________ R_________ ( P) would result in a rotation of -174°.
l
m
87°
41°
A
c) R_________ R_________ ( P) would result in a rotation of 256°.
60. What rule would establish that these two polygons are congruent to each other?
a) Begin with ∆CDE
R ( x, y ) − − > (______, _____)
61.Given coordinate rule
T ( x, y ) − − − − > (− x 2 , −5)
determine the image of A(-2,2)?
b) Begin with ∆CDE
P ( x, y ) − − > (______, _____)
c) Begin with Quad CDGH
L ( x, y ) − − > (______, _____)
62. Given coordinate rule,
T ( x, y) − − − − > ( x + 2, y − 6)
determine the pre-image of A’(-2,2)?
63. Jeff claims that all squares would be isometric transformations because every square has four equal sides
and four equal angles. Is he correct? Explain your answer.
Test 1 Review
6
64. Given the shape, shade it so that it has reflectional symmetry.
a) 1 line of symmetry
b) 2 lines of symmetry
c) Order 4
d) Order 4
65. ABC is reflected over line g to create the image ∆A’B’C’. What is the relationship between AA ' , BB ' and
CC ' ?
66. ∆ABC is mapped by a single isometric transformation to ∆A’B’C. Name ALL of the isometric
transformations that could have performed this? Explain why you chose the one(s) you did.
67. What are the coordinate rules for the given transformations?
REFLECTION RULES
ROTATION RULES
Ry axis ( x, y ) = (______, ______)
RO ,90° ( x, y ) = (_____, _____)
Rx axis ( x, y ) = (______, ______)
RO ,180° ( x, y ) = (_____, _____)
Ry = x ( x, y ) = (______, ______)
RO ,270° ( x, y ) = (_____, _____)
68. What are the characteristics of the given transformations?
CHARACTERISTIC
ISOMETRIC?
DISTANCES (all points
move the same distance)
OREINTATION?
CAN A = A’?
REFLECTION
YES OR NO
YES OR NO
ROTATION
YES OR NO
YES OR NO
TRANSLATION
YES OR NO
YES OR NO
SAME OR REVERSE
YES OR NO
SAME OR REVERSE
YES OR NO
SAME OR REVERSE
YES OR NO
Test 1 Review
7
69. What are the missing measures in Parallelogram SRQP?
m∠9 = 66˚
m∠2 = 14˚
m∠1 = 16˚
Q
m∠6 = ________
9
m∠10 = ________
m∠11 = ________
m∠3 = ________
11
8
7
S
6
70. Perform the following on the grid.
a)
1
6
T
10
2
P
5
4
3
A
D
RM ,90° ( NOPQ)
4
C
H
b) RF ,180° ( ∆GHI )
2
E
M
N
B
c) RAB (∆CDE )
10
G
d)
I
O
J
5
5
K
F
T〈 3,2 〉 (∆JKL)
2
Q
P
L
4
71. Determine the smallest positive angle of rotation that would perform the same rotation as the given one.
a)
R0,−50° = R0,_______ °
b)
R0,400° = R0,_______ °
c)
R0,−730° = R0,_______ °
72. Determine the name of the point that meets the given conditions.
a)
Rn ( A) =
c)
RO ,−90° ( D) =
e)
T DF ( H ) =
g)
Rm (G ) =
________
________
________
________
b)
Rr (C ) =
d)
Rm (______) = B
f)
RO ,90° ( E ) =
h)
RG ,180 (______) = C
________
________
73. Use your rules to solve these.
a)
Rx axis A(5, 4) = A '(_______, _______)
b)
Ry axis Rx axis A(−5,1) = A ''(______, ______)
c)
Rx axis R y axis A(_______, _______) = A ''(4, − 3)
d)
T〈−3,5〉 A(_______, _______) = A '(9, −3)
e)
T〈−2, −1〉 Ry axis A(5,3) = A ''(_______, _______)
f)
Rx axis A( −1, 6) = A '(_______, _______)
g)
RO ,90 A(3, 2) = A '(_______, _______)
h)
RO ,90° A(_______, _______) = A '(8, 3)
R
Test 1 Review
8
74. Construct the following Rm ( ∆ABC )
and
RA,100° (∆BCD)
D
B
m
C
B
C
A
A
75. Determine whether the following are congruent or not. If they are congruent, state the reason for
congruence (SSS, SAS, ASA, AAS, HL) If they are not congruent simply circle NO.
a) Yes or No
REASON: __________
b) Yes or No
REASON: __________
c) Yes or No
REASON: __________
d) Yes or No
REASON: __________
e) Yes or No
REASON: _________
f) Yes or No
REASON: _________
g) Yes or No
REASON: _________
h) Yes or No
REASON: _________
76) GIVEN:
77) GIVEN:
CB || ED & CA ≅ DA
AB || CD & BC || DE
&
PROVE:
CD ≅ AB
BA ≅ EA
PROVE:
STATEMENT
REASON
∆ABC ≅ ∆CDE
STATEMENT
REASON
Test 1 Review
9
78. Solve for the unknown values.
a) x = ___________
b) x = ___________
c) x = ___________
9x - 11
5x + 25
d) x = ________
e) x = ________
7x + 15
f) x = ________
41°
126°
35°
89°
x
x
165°
x
g) x = ________
h) x = ________
i) x = ________
x
x
32°
53°
x
x
x
79. Complete the following:
a) If ∆DOG is isosceles and OG ≅ OD , then the base angles are ________ and _______.
b) If two angles of a triangle are 48 & 67, then the 3rd angle is ________.
c) If one remote angle is 55° and the exterior angle is 135°. What is the other remote angle? _________
d) What is the full name of the ∆ABC with the following given information?
-- m∠A = 60°, m∠B = 80°, m∠40° _______________________________________________
-- AB = AC & m∠A = 130°
________________________________________________
-- AB > BC > CA
________________________________________________
Test 1 Review
10
1. C 2. B 3. A 4. B 5. C 6. D 7. D 8. A 9. B 10. C 11. B 12. B 13. A 14. D 15. B 16. C 17. D 18. C 19. D
20. D 21. B 22. D 23. D 24. B 25. B 26. D 27. A 28. A 29. B 30. C 31a. P 31b. HJ 31c. F 31d. OM 32. T
33. T 34. F 35. F 36. T 37. F 38. F 39. T 40. F 41. T 42. F 43. T 44. F 45. F 46. F 47. F 48. T 49. F 50. T
51. T 52. T 53. F 54. F 55. F 56. T 57. T 58. T 59a. k,m 59b. k,l 59c. l,m 60a. ( x + 8, y − 2 ) 60b. ( − y , x )
60c. ( − x, y ) 61. (-4,-5) 62. (-4,8) 63. No, not all squares would have congruent sides.
64.
65. They are all parallel 66. rotation, reflection
67.
68. Isometric: Y,Y,Y; Distances: N,N,Y; Orientation: R,S,S; A=A’: Y,Y,N 69. 14, 114, 66, 100
70.
71a. 310 71b. 40 71c. 350 72a. B 72b. A 72c. A 72d. D 72e. B 72f. H
72g. H 72h. B 73a. (5,-4) 73b. (5,-1) 73c. (-4,3) 73d. (12,-8) 73e. (-7,2)
73f. (-1,-6) 73g. (-2,3) 73h. (3,-8)
74.
75a. No 75b. Y, SAS 75c. Y, HL
75d. Yes, AAS 75e. Yes, SAS 75f. Yes, SAS
75g. Yes, ASA 75h. Yes, ASA or AAS
76.
77.
78a. 23 78b. 13 78c. 11 78d. 36 78e. 76 78f. 76 78g. 74 78h. 74
78i. 60 79a. ∠G & ∠D 79b. 65 79c. 80
79d. Acute Scalene, Obtuse Isosceles, Scalene