Name: _______________________
Similar Triangles: Day 1
Date: ____ Period:____
Ms. Anderle
Similar Triangles: Day 1
Two triangles that are the same shape, but not the same size are said to be similar.
The symbol for similar triangles is ~. Similar triangles have angles that are
congruent and sides that are in proportion.
Scale Factor/Ratio of Similitude:
When you compare the lengths of corresponding sides of similar triangles, you
usually get a numerical ratio. This ratio is called the scale factor or the ratio of
similitude for the two triangles.
When finding the scale factor for two similar polygons, it will depend on the order
of comparison. If the question does not ask you to compare one polygon to the
other, either way is correct.
Examples:
1) ∆ABC ~ ∆DEF
A
6
D
12
B
Find e and the ratio of similitude:
18
e
C
E
2) ∆RPQ ~ ∆IGH
R
I
3
P
F
Find the scale factor and x:
8
4
Q
G
x
H
3) ∆RAY ~ ∆TOM
R
x
A
T
Find the ratio of similitude and x:
5
2
O
Y
x+3
M
Other figures can be considered similar as well. The process in finding the ratio of
similitude and the scale factor is exactly the same. Two polygons are similar if
their corresponding angles are congruent and the measure of their corresponding
sides are proportional.
4) Quad ABCD ~ Quad EFGH (<A ≅ <E, <B ≅ <F, <C ≅ <G, <D ≅ <H)
A
E
5
10
B
D
2.5
C
F
H
y
G
Find the ratio of similitude between Quad EFGH to Quad ABCD
What is the value of y?
5) ABCDE ~ RSTUV (<A ≅ <R, <B ≅ <S, <C ≅ <T, <D ≅ <U, <E ≅ <V)
A
4
R
B
E
C
6
V
S
D
y+1
T
U
8
Find the scale factor of polygon ABCDE to polygon RSTUV
What is the value of y?
5) MATH ~ GEOS (<M ≅ <G, <A ≅ <E, <T ≅ <O, <H ≅ <S)
2
M
A
x
T
E
S
x+1
H
G
6
What is the ratio of similitude?
Find the value of x:
O
6) A triangle has side lengths of 3 meters, 5 meters, and 4 meters. The triangle is
enlarged so that the larger triangle is similar to the original and the scale factor is
5. Find the perimeter of the larger triangle.
7) ∆MAY ~ ∆BOW (<M ≅ <B, <A ≅ <O, <Y ≅ <W)
M
B
b+2
Y
1
8
15
A
O
10
W
Find the ratio of similitude of ∆BOW to ∆MAY
What is the value of b?
8) The sides of a triangle are 5, 6, and 10. Find the length of the longest side of a
similar triangle if the shortest side is 15.