Chapter 8
1. Solve the proportions.
a) y =
9
4
6
b)
7
= 4
3n + 5
n
2. The ratio of the two side lengths of the triangle is given. Solve for the variable.
a) AB:BC is 2: 5
b) MN:MO is 3:4
M
A
x
x
B
O
20
9
C
N
3. The lengths of the sides of a triangle are in the extended ratio of 2:3:5. If the perimeter
is 70 inches, find the lengths of each side.
Equation: ______________________
Sides: ________ , ________, ________
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4. Find the geometric mean of the two numbers.
5 and 20
4 and 9
5. Given: ∆ABC ~ ∆DEC, and BE = 6, EC = 8, DC = 10 and AB = 12.25
Find the lengths of DE and AD
B
6
E
12.25
8
A
D
C
10
a. Find DE
DE= _______
b. Find AD
AD= _______
6. In the diagram below, parallelograms RSTU Ӵ LMNO.
R
12
S
L
M
9
U
72°
T
3
O
N
a) Find the ratio of sides of RSTU to LMNO.
b) Find the ratio of sides of LMNO to RSTU.
c) Find LM
d) Find mӘO
e) Find the ratio of the perimeter of parallelogram RSTU to the perimeter of
parallelogram LMNO.
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7. Use the pairs of triangles below.
a) Decided if the triangles below are similar.
b) If yes, state the postulate or theorem and use proportions if necessary.
c) If the triangles are similar write a similarity statement.
8. Determine whether the given information implies BC // DE. Explain your answer.
(Figure not drawn to scale)
A
6
D
9
B
4
E
6
C
9. Last December, the exchange-rate for Canadian dollars to American dollars was
$1.47 Canadian to $1.00 American. If you paid $55.00 Canadian dollars for a
sweatshirt, what did the shirt cost you in American dollars?
10. A 5 x 7 inch photo is being enlarged by a scale factor of 11 . What are the dimensions
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of the enlarged photo? Round your answers to the nearest tenth.
_______ in. by _______ in.
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11. Use your knowledge of similar triangles and proportionality theorems to find the values
of the variables below.
a) Given: ¨ABC Ӵ¨DEC find the value of x and y.
b) Given: WX bisects Ә; find the value of a.
c) Find the value of a in the figure below.
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12. The larger triangle is an enlargement of the smaller triangle. What is the scale factor?
Solve for x and y.
13. Use the given scale factors to find the coordinates of the vertices of the image of the
¨ XYZ.
k X ( ___, ___)
Y ( ___, ___)
Z ( ___, ___)
X’ ( ___, ___)
Y’ ( ___, ___)
Is this an enlargement
Z’ ( ___, ___)
or a reduction? (Circle one.)
k ò
X ( ___, ___)
Y ( ___, ___)
Z ( ___, ___)
X’ ( ___, ___)
Y’ ( ___, ___)
Is this an enlargement
Z’ ( ___, ___)
or a reduction? (Circle one.)
11