Download ACDM Unit 6 Part 4 - Similarity and Scale

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AAG ACADEMIC
Unit 6 Part 4 – Similarity and Scale Factor
When you draw a diagram of a large object, you don’t need an enormous piece of paper. You use a convenient
sheet and draw to scale. You would show the correct shape, but in a size that would fit your piece of paper.
Two figures that have the same shape and size are called similar.
Two polygons are similar if their vertices can be paired so that:
1) Corresponding angles are congruent, AND
2) Corresponding sides are in proportions (lengths have the same ratio).
When you refer to similar polygons, their corresponding vertices must be listed in the same order. If polygon
ABCDE is similar to polygon VWXYZ, you write:
C
ABCDE
B
V
VWXYZ
D
W
20
Z
X
A
32
E
Y
Using the definition of similar polygons, list the following:
- All congruent angles:
- All proportional sides:
If two polygons are similar, then the ratio of the lengths of two corresponding sides is called the scale factor
of the similarity.
List the scale factor of:
ABCDE to VWXYZ
VWXYZ to ABCDE
S
1) Given: △SPA △△GEL .
G
A) List all congruent angles.
P
A
E
B) Write the ratios of the corresponding sides in a statement of proportionality.
C) If
and
, find all remaining angle measures.
D) If SP = 10, PA = 20, GE = 16, and GL = 24, find the remaining side lengths.
E) List the scale factor of:
△SPA to △GEL
F) Find the perimeter of each triangle.
△GEL to △SPA
G) Find the ratio of the perimeters.
L
2) Given: Parallelograms
with side lengths and angles marked.
A) Write the ratios of the corresponding sides in a statement of proportionality.
X
B) Find all missing angle measures.
Y
48
60°
W
Z
O
C) Find all missing side lengths.
P
120°
24
N
32
D) Find the perimeter of WXYZ and MNOP.
E) Find the ratio of the perimeter of WXYZ to MNOP.
F) Find the ratio of the perimeter of MNOP to WXYZ.
M
Directions: Determine whether the triangles are similar. If they are, write a similarity statement.
3)
4)
J
5)
6) Given: GH / /IJ .
G
K
H
I
7) Consider the diagram below to answer the following questions.
EA = 3.71 cm
A) Write a similarity statement for the diagram to the right.
E
A
△
~ △
EF = 8.76 cm
AD = 7.67 cm
B) Write a statement of proportionality.
y
D
GD = 5.61 cm
G
x
C) Solve for x.
D) Solve for y.
F
Redraw the triangles below……..
8) If
△FGH △△JKL , set up a proportion and solve for x.
G
5x
3x + 2
H
F
K
7x
5x - 2
L
J
9) If
, what is the length of DV?
P
x
x+8
U
T
D
x-3
x+3
R
V
10) An airplane has a wingspan of (x 2  1) ft and a length of (x 2  9) ft. A scale model of this plane has a
wingspan of (x  3) and a length of (x  1) ft. Based on this information, use a proportion to find the wingspan
of the actual plane.
11) The community park has a rectangular swimming pool enclosed by a rectangular fence for sunbathing. The
shape of the pool is similar to the shape of the fence. The pool is 30 feet wide. The fence is 50 feet wide and
100 feet long.
A) What is the ratio of the side lengths of the pool to the fence?
B) What is the length of the pool?
C) Find the area reserved strictly for sunbathing.
Directions: Consider the figure, where IK / /HL to the right to answer the following questions.
12) Name all pairs of congruent angles.
J
14)
9
6
13) △IKJ △
?
9
and x =

x 24
I
12
y
K
15
x
L
H
15)
9
6
 and y =
24 ?
16) Is
JI JK
a true statement?

IH
KL
Property of Proportions: If the cross-products of a proportion are equivalent, than the proportion is
equivalent.
a c
is equivalent to:

b d
Side-Splitting Theorem:
A) If a line is
points, it splits these sides into
to a side of a triangle and intersects the other two sides in distinct
segments.
B) If a line intersects OP and OQ in distinct points X and Y so that
OX OY

then XY is
XP YQ
to PQ . Draw a picture to illustrate your this situation.
17)
18)
19) If ST / /UV , set up a proportion and solve for x.
R
4x
S
5x
T
8x - 4
12x + 7
U
V
20)
21)