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Geo
Unit 6 Similarity/Ratio/Proportion Test Review
1. In the diagram below, ∆ABC : ∆EDC.
Find the value of x, the length AC and the length EC.
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"
"
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x = _______ AC = ________ EC = _______
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2. "
ΔXYZ ~ ΔABC , ∠X = 20° , ∠A = 3x + 2y ° , ∠Z = 16x − y ° , ∠Y = 5x + 5y ° .
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(
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(
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(
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Draw the two triangles and find the measures of all the angles.
3. The shadow of a tree is 2500 cm long. At the same time, a person who is 180 cm tall
casts a shadow 240 cm long. How tall is the tree?
x
180 cm
2500 cm
240 cm
4. Write a statement reason proof:
A
Given: ∠ AED ≅ ∠ ABC
D
Prove: ∆DAE
E
B
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~ ∆CAB
C
Statement" "
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Reason
b) AD = 9, AB = 16, DE = 5, AE = 4, find EC, and BC.
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EC = ________" "
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BC = ________
5. EM || CF , LC = 12, LF = 16, CF = 22 and CE = 3. Find EM.
L
M
E
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F
C
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"
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EM = __________
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RS = ___________
6. TS || PQ , RP = 8, RT = 6, RQ = 12. Find RS.
R
T
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P
S
Q"
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7. TS || PQ , RP = 6, RT = 4 and RQ = 9. Find RS.
R
T
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S
Q
P
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RS = ___________
50 2
= "
x 5
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C.
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5x 2 −6x + 1
F.
=
−1
1
8. Solve these equations :
x 1
= "
9 9
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A.
"
x 5
D.
= "
5 x
"
"
"
B.
"
3+ x 3− x 5
E.
−
= ""
2
3
6
x 2 2x + 3
=
−4
1
9.
B
2
A. Mark one more thing in the diagram and then redraw
the triangles separately.
C
B.
6
_________ ~ __________
C. Set up a proportion and solve for x.
A
x
D
2
E
10. LG ⊥ WJ , DJ ⊥ WJ , LG = 4, WJ = 20 and DJ = 15.
A. Find WG. "
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B. Use what you found in part a to find LW."
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WG = _______
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LW = ________
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"
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RC = _______
"
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RS = ___________
D
L
G
W
J
11. GC = 9, JC = 15 and DC = 6. Find RC.
R
G
J
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D
C
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12. TS || PQ , TP = 4, RT = 7 and SQ = 5. Find RS.
R
T
P
S
Q"
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13 a)
b) The lengths of the sides of a triangle are 16, 20 and 24. The triangle is similar to
another one whose perimeter is 24. Draw and label the triangles and find the lengths of all
sides of the second triangle.
14. Write a statement/reason proof.
M
Given: ∠ M = ∠ ABQ
B
Prove: ∆MPQ ~ ∆BAQ
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P
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Statement" "
15.
Q
A
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Reason
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16.!
Solve for x in part a and part b. What do you notice?
17. While at the zoo, you put a mirror near the giraffe area and stand back until you can see the top
of the giraffe in the mirror. If you are 5 feet from the mirror and the mirror is 15 feet from the giraffe
you are looking at, how tall is the giraffe if you are 5'3" ?
18. In each case, draw a diagram and explain your answer!
Indicate whether or not the statement is true ALWAYS, SOMETIMES or NEVER.
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a) Two isosceles triangles are similar if a base angle of one is congruent to a base angle of the
other.
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b) Two isosceles triangles are similar if the vertex angle of one is congruent to the vertex
angle of the other.
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c) Two right triangles are ________________ similar.