1. Perimeters and SimilarityPerimeters and Similarity
You will learn to identify and use proportional relationships of
similar triangles.
1) Scale Factor
2. Perimeters and SimilarityPerimeters and Similarity
These right triangles are similar!
Therefore, the measures of their corresponding sides are ___________.
Is there a relationship between the measures of the perimeters of the two
triangles?
8
6
10
12
15
9
proportional
We know that
6
9
8
12
10
15
= =
Use the ____________ theorem
to calculate the length of the
hypotenuse.
Pythagorean
222
bac +=
2
3
=
perimeter of small Δ
perimeter of large Δ
=
9 + 12 + 15
6 + 8 + 10
=
36
24
=
3
2
3. Perimeters and SimilarityPerimeters and Similarity
perimeter of ΔABC
perimeter of ΔDEF
=
DE
AB
=
Theorem
9-10
If two triangles are similar, then
A
C B
F E
D
the measures of the
corresponding perimeters are proportional to the measures
of the corresponding sides.
If ΔABC ~ ΔDEF, then
EF
BC
=
FD
CA
4. Perimeters and SimilarityPerimeters and Similarity
27 = 13.5x
The perimeter of ΔRST is 9 units, and ΔRST ~ ΔMNP.
Find the value of each variable. M
N
4.5
P
R
S
T 3
6
z
Y
x
perimeter of ΔMNP
perimeter of ΔRSTRS
MN
=
13.5
9x
3
=
Theorem 9-10
The perimeter of ΔMNP is 3 + 6 + 4.5
Cross Products
x = 2
RS
MN
=
ST
NP
RS
MN
=
TR
PM
2
3
=
y
6
2
3
=
z
4.5
3y = 12 3z = 9
y = 4 z = 3
5. Perimeters and SimilarityPerimeters and Similarity
DE
AB
=
EF
BC
FD
CA
=
Each ratio is equivalent to
2
1
If ΔABC ~ ΔDEF, then
The ratio found by comparing the measures of corresponding sides of
similar triangles is called the constant of proportionality or the ___________.scale factor
A
B C7
5
3
D
E F14
10
6
or
6
3
=
14
7
=
10
5
The scale factor of ΔABC to ΔDEF is
2
1
The scale factor of ΔDEF to ΔABC is
1
2
