1. 9.2 Similar Polygons

2. Vocabulary What You'll Learn Similar Polygons
You will learn to identify similar polygons.
Vocabulary
1) polygons
2) sides
3) similar polygons
4) scale drawing

3. Polygons that are the same shape but not necessarily the same size are
Similar Polygons
A polygon is a ______ figure in a plane formed by segments called sides.
closed
It is a general term used to describe a geometric figure with at least three sides.
Polygons that are the same shape but not necessarily the same size are
called ______________.
similar polygons
The symbol ~ is used to show that two figures are similar.
ΔABC is similar to ΔDEF A B C D F E
ΔABC ~ ΔDEF

4. Similar Polygons
Definition of
Similar
Polygons
Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are ___________.
proportional C D A B F E G H
and
Polygon ABCD ~ polygon EFGH

5. Determine if the polygons are similar. Justify your answer.
Similar Polygons
Determine if the polygons are similar. Justify your answer. 7 6 6 4 5 4 5 7
1) Are corresponding angles are _________.
congruent
2) Are corresponding sides ___________.
proportional =
0.66 = 0.71
The polygons are NOT similar!

6. Find the values of x and y if ΔRST ~ ΔJKL
Similar Polygons
Find the values of x and y if ΔRST ~ ΔJKL R T S J L K 4 5 6 7 x
y + 2
Write the proportion that can be solved for y. 4 6 =
y + 2 7
Write the proportion that can be solved for x.
4(y + 2) = 42
4y + 8 = 42 4 5 =
4y = 34 7 x
4x = 35

7. Contractors use scale drawings to represent the floorplan of a house.
Similar Polygons
Scale drawings are often used to represent something that is too large or too small to be drawn at actual size.
Contractors use scale drawings to represent the floorplan of a house.
Dining
Room
Kitchen
Living
Garage
Utility
1.25 in.
.75 in.
1 in.
.5 in.
Scale: 1 in. = 16 ft.
Use proportions to find the actual
dimensions of the kitchen.
width
length
1 in
1.25 in.
1 in
.75 in. = =
16 ft
w ft.
16 ft
L ft.
(16)(1.25) = w
(16)(.75) = L
20 = w
12 = L
width is 20 ft.
length is 12 ft.

8. Perimeters and Similarity
What You'll Learn
You will learn to identify and use proportional relationships of
similar triangles.
Vocabulary
1) Scale Factor

9. Perimeters and Similarity
These right triangles are similar! Therefore, the measures of their corresponding sides are ___________.
proportional
Use the ____________ theorem to calculate the length of the
hypotenuse.
Pythagorean 10 6 15 9 8 12 6 8 10 2
We know that = = = 9 12 15 3
Is there a relationship between the measures of the perimeters of the two
triangles?
perimeter of small Δ
perimeter of large Δ = = 36 24 = 3 2

10. Perimeters and Similarity
Theorem
9-10
If two triangles are similar, then
the measures of the
corresponding perimeters are proportional to
the measures
of the corresponding sides. A C B F E D
If ΔABC ~ ΔDEF, then
perimeter of ΔABC
perimeter of ΔDEF = DE AB = EF BC = FD CA

11. Perimeters and Similarity
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 ΔRST RS MN = RS MN = ST NP RS MN = TR PM
Theorem 9-10 2 3 = y 6 2 3 = z
4.5
13.5 9 x 3 =
The perimeter of ΔMNP is
3y = 12
3z = 9
27 = 13.5x
Cross Products
x = 2
y = 4
z = 3

12. Perimeters and Similarity
The ratio found by comparing the measures of corresponding sides of
similar triangles is called the constant of proportionality or the ___________.
scale factor D E F 14 10 6 A B C 7 5 3 DE AB = EF BC FD CA
If ΔABC ~ ΔDEF, then or 6 3 = 14 7 10 5 2 1
The scale factor of ΔABC to ΔDEF is 2 1
Each ratio is equivalent to 1 2
The scale factor of ΔDEF to ΔABC is

13. End of section 9.2