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Name _________________________ Period _____ 1
UNIT 2 REVIEW 2
1. Which of the following is a non-isometric transformation?
A) Stretch
B) Translation
C) Rotation
D) Reflection
2. A reflection of ∆ABC creates image #1 and a dilation of scale factor of 5 of ∆ABC creates image #2. Which of the following is NOT
true about image #1 and image #2?
A) Angles will be congruent.
3. If we
D
O,
B) Sides will be congruent
C) Orientation will be reversed.
D) Shape will be the same
then the correct diagram would be:
1
2
Original
A)
B)
m
O
C)
m
m
m'
O
O
D)
m
m
m'
O
O
4. Determine the scale factor that best suits the provided diagram (O is the center of dilation).
B'
A) 2
B)
1
2
C)
1
3
A'
D) - 1
5x
3x
o
o
B) SAS
C) SSS
6 cm
D) Not enough info or not similar
6. In the given diagram, which of the following statement is NOT true:
A)
AB BC
=
BE CF
B)
GB GE
=
AC DF
C)
AD GD
=
BE GE
G
D)
DF DE
=
AC
AB
D
A
E
B
F
C
7. The ratio of the short leg to the long leg in a 30° right triangle is:
A) 1 : 2
8. The ratio
B) 1 :
3
C) 2 : 1
D)
3 :1
6 represent the which relationship:
10
B
6 cm
10 cm
A
A) sin ∠C
B) sin ∠B
C) tan ∠C
D) cos ∠C
9. The geometric mean of 8 and 18 is:
A) 13
B) 12
C) 11
D) cannot be determined
8 cm
B
O
A
5. Which of the following would be the criterion for establishing similarity in the two triangles?
A) AA
m'
C
10 cm
UNIT 2 REVIEW 2
2
10. Which of the following statements is false?
A) sin 45° = cos 45°
B) sin 30° = cos 30°
C) cos 10° = sin 80°
11. The value for x is:
D) sin 0° = cos 90°
o
A) 7 2
B) 14
C) 14 2
14 2
D) 28
o
x
12. The value for x is:
x
A) 10
B) 10 6
C) 12 3
60°
D) 20
10 3
13. Julie has a large red apple in her hand that is 4 ft off the ground. A blue bird sees
the apple at an angle of depression of 55°. If Julie is 15 ft from the tree, how tall is the
tree (round to the nearest foot)??
A) 16 ft
B) 17 ft C) 21 ft
D) 25 ft
14. For angles between 0° and 90° the sine values are between 0 and 1.
T or F
15. All right triangles are similar.
T or F
16. If in ∆ABC & ∆GHY,
AB
BC CA then ∆ABC ∼ ∆GHY.
=
=
GH HY YG
T or F
17. If ∆ABC ∼ ∆DEF, then m∠ABC = m∠FED
T or F
18. DO ,2 (∠ ABC ) = ∠ A ' B ' C ' , then m∠A’B’C’ = 2 (m∠ABC).
T or F
19. Given DO ,2.5 P (4, −8) then P '(10, 20)
T or F
20. sin (2x – 7) = cos (x + 13) when x = 28.
T or F
Solve for the unknown.
21. sin (x)= cos (x)
22. sin ( 1 x ) = cos ( 2 x + 3 )
5
5
Determine the Geometric Mean of the two given numbers. (Exact Answers Only)
23.
8 and 18
24.
50 and 8
UNIT 2 REVIEW 2
3
Find the missing values. (If not a whole number, leave it in simplest radical form)
25.
x+2
5
x
x = ________ y = _________
z = ________
26. The horizontal distance of the ramp is 12 ft and the vertical height of the ramp is 4
ft. What is the length of the ramp? (2 decimal places)
27. A helicopter is hovering 200 ft in the air over a landing pad. If the man sees the helicopter at
an angle of elevation of 38°, how far is he from the landing pad (to the nearest foot)??
28. A flagpole is at the top of a building. 100 ft from the base of the building, the angle of elevation
of the top of the pole is 42° and the angle of elevation of the bottom of the pole is 39°. Determine
the length of the flagpole (to the nearest foot).
UNIT 2 REVIEW 2
4
29. From a lighthouse 460 ft above sea level, the angle of depression to a boat (A) is
42°. Sometime later the boat has moved closer to the shore (B) and the angle of
depression measures 50°. How far (to the nearest foot) has the boat moved in that
time?
30. Determine the sequence of similarity transformations that map
one figure onto the other, establishing that the two figures are
similar.
Determine two similarity transformations that would map Quad.
OKBC onto Quad. OYPL.
________________ followed by _________________
Complete the following. (When calculating the slope do not simplify it in any way!! The slope is actually a vector.)
31. Center of dilation is G.
Scale Factor 3
Determine the slope of
m=
y2 − y1
x2 − x1
Determine A’.
G (4,1)
A (5,9)
GA from G ( x1 , y1 ) to A ( x2 , y2 )
UNIT 2 REVIEW 2
5
Given the dilation centered at O,
A
A'
32. If AB = 10 cm and A’B’ = 4 cm, what is the scale factor of the dilation?
O
B'
B
Are the following pairs of triangles similar? If they are, then
name their similarity criteria. (SSS, SAS, AA)
Find the values for the missing variables.
34.
12
33. Yes / No __________
x
o
o
10.5
3.5
x = __________
35. Solve – The area of a rectangle is 504 cm2. If the length and the width are in a ratio of 7:2. (2 points)
_______ & _______
36. When looking at a trigonometry table Donna notices that the Tangent ratio for the 45° right triangle is 1. Explain why that
happened.
UNIT 2 REVIEW 2
6
Solve for the missing information. (Round all final answers to 2 decimals places)
37.
38.
63°
9 cm
12 cm
θ°
14 cm
x
x ≈ ____________
Ɵ = ____________
G
39. GIVEN: ∠F ≅ ∠HJI
J
o
PROVE: GH ◦ JH = FH ◦ IH
o
F
STATEMENT
40. Use a compass and a straightedge to construct
A
O
D
B
I
H
REASON
DO ,3 ( ∆ADB )
UNIT 2 REVIEW 2
7
1.A
2. B
3. A
4. B
5.B
6. A
16. T
17. T
18. F
19. F
20. T
21. x=45
27. 256 ft
28. 9 ft
29. 125 ft
7. B
8. A
9. B
22. x=145
30.various answers
10. B 11. B 12. D 13. D 14. T
23. 12 24. 20 25. x=4
31. m= 8; A’(7,25)
15. F
26. 12.65 ft
32. 2/5 33. Yes AA
34. x=3
35. 42 and 12 36. A 45° right triangle is an isosceles triangle with congruent legs. These two
congruent legs are the opposite and the adjacent for the 45° angle so opposite / adjacent = 1.
37. 10.10 cm 38. 59°
39.
STATEMENT
REASON
∠F ≅ ∠HJI
Given
∠H ≅ ∠H
Reflexive Prop. (Common ∠)
∆HGF ∼ ∆HIJ
AA
GH FH
=
IH
JH
∆HGF ∼ ∆HIJ
(prop. sides of ∼ ∆)
GH ◦ JH = FH ◦ IH
Cross Multiplication
40.