1. Geometry
8.3 Similar Polygons

2. Geometry 8.3 Similar Polygons
Goals
Identify similar polygons
Find the ratio of similarity between similar figures.
Solve problems involving similar figures.
May 31, 2018
Geometry 8.3 Similar Polygons

3. Geometry 8.3 Similar Polygons
ABCD and RSTV are similar polygons:
Corresponding angles are congruent.
Corresponding sides are proportional. A B C D 15 12 9 R S T V 10 8 6 6
May 31, 2018
Geometry 8.3 Similar Polygons

4. Geometry 8.3 Similar Polygons
Corresponding angles are congruent:
A  R, B  S, C  T, D  V A B C D 15 12 9 R S T V 10 8 6 6
May 31, 2018
Geometry 8.3 Similar Polygons

5. Geometry 8.3 Similar Polygons
Corresponding sides are proportional: A B C D 15 12 9 S 6 R 6 T 10 8 V
May 31, 2018
Geometry 8.3 Similar Polygons

6. Geometry 8.3 Similar Polygons
Corr. s 
Sides prop.
ABCD ~ RSTV A B C D 15 12 9 R S T V 10 8 6 6
May 31, 2018
Geometry 8.3 Similar Polygons

7. Geometry 8.3 Similar Polygons
Corresponding Angles are congruent.
Corresponding Sides are proportional.
Use the symbol “~” for similar.
To show that two polygons are similar, you must prove both things: angles congruent, sides proportional.
May 31, 2018
Geometry 8.3 Similar Polygons

8. Similarity Statements
List the congruent angles.
Write the ratios of the corresponding sides.
J  Q, K  S, L  R
70 J K L Q R S
May 31, 2018
Geometry 8.3 Similar Polygons

9. Geometry 8.3 Similar Polygons
Example
Are these figures similar?
Yes
Why?
Corr. angles congruent
Corr. sides proportional. 3 E F 2
1.5 H G 4 N 6 M 4 3 O 8 P
May 31, 2018
Geometry 8.3 Similar Polygons

10. Write the similarity statements.3 E F 2
1.5 H G 4 N 6 M 4 3 O
EFGH ~ NMPO 8 P
Or: HEFG ~ ONMP, GFEH ~ PMNO, EHGF ~ NOPM, etc.
May 31, 2018
Geometry 8.3 Similar Polygons

11. Geometry 8.3 Similar Polygons
Scale Factor
If two polygons are similar, the ratio of two corresponding sides is called the scale factor.
May 31, 2018
Geometry 8.3 Similar Polygons

12. Geometry 8.3 Similar Polygons
Scale Factor
The scale factor of JKL to QSR is 10/5 or 2/1.
The scale factor of QSR to JKL is 5/10 or 1/2.
70 J K L Q R S 10 5
May 31, 2018
Geometry 8.3 Similar Polygons

13. Perimeter and Similar Figures
ABCD ~ FGHI
Find the scale factor of ABCD to FGHI.
Find the values of x, y, and z.
Find the perimeter of ABCD and FGHI.
Find the ratio of the perimeters. A B C D F G H I 10 4 14 5 z y x
May 31, 2018
Geometry 8.3 Similar Polygons

14. Perimeter and Similar Figures
2. Find the scale factor from ABCD to FGHI.
The only known corresponding sides are AB and FG. A B C D F G H I 10 4 14 5 z y x
May 31, 2018
Geometry 8.3 Similar Polygons

15. Perimeter and Similar Figures
3. Find the values of x, y, and z. A B C D F G H I 10 4 14 5 z y x
May 31, 2018
Geometry 8.3 Similar Polygons

16. Perimeter and Similar Figures
4. Find the perimeter of ABCD and FGHI.
P = 42
P = 21 A B C D F G H I 10 4 14 5 2 7
May 31, 2018
Geometry 8.3 Similar Polygons

17. Perimeter and Similar Figures
5. Find the ratio of the perimeters.
Ratio of perimeters 2:1
Ratio of Similarity 2:1
P = 42
P = 21 A B C D F G H I 10 4 14 5 2 7
May 31, 2018
Geometry 8.3 Similar Polygons

18. Geometry 8.3 Similar Polygons
Theorem 8.1
If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths and is equal to the similarity ratio.
May 31, 2018
Geometry 8.3 Similar Polygons

19. Geometry 8.3 Similar Polygons
Theorem 8.1 Example
These figures are similar. Find the perimeter of the smaller one. 20 8
P = 100
P = ?
May 31, 2018
Geometry 8.3 Similar Polygons

20. Geometry 8.3 Similar Polygons
Problems to Solve
May 31, 2018
Geometry 8.3 Similar Polygons

21. Geometry 8.3 Similar Polygons
Problem 1
Solve for x and y if the triangles are similar. 20
x + 6 8 4
y – 2 6
May 31, 2018
Geometry 8.3 Similar Polygons

22. Geometry 8.3 Similar Polygons
Problem 1 Solution
Scale Factor is 20/8 20
x + 6 8 4
y – 2 6
Solve
for x
Solve
for y
May 31, 2018
Geometry 8.3 Similar Polygons

23. Geometry 8.3 Similar Polygons
Problem 2
Find x and y if the figures are similar.
x + 10
85
100 32 60 24 y
95
May 31, 2018
Geometry 8.3 Similar Polygons

24. Geometry 8.3 Similar Polygons
Problem 2 Solution 60
x + 10
95
85
100 y 24 32
Similarity Ratio
y = 360 - 100 - 85 - 95
y = 80
May 31, 2018
Geometry 8.3 Similar Polygons

25. Geometry 8.3 Similar Polygons
Problem 3
ABC ~ RST
AB = 20
ST = 4
BC = RS
Find BC and RS.
May 31, 2018
Geometry 8.3 Similar Polygons

26. Geometry 8.3 Similar Polygons
Problem 3 Solution A B C R S T
ABC ~ RST
AB = 20
ST = 4
BC = RS
Find BC and RS. 20 x 4 x
May 31, 2018
Geometry 8.3 Similar Polygons

27. Geometry 8.3 Similar Polygons
Problem 3 Solution A B C R S T 20 4 x
ABC ~ RST
May 31, 2018
Geometry 8.3 Similar Polygons

28. Geometry 8.3 Similar Polygons
Problem 4
You want to print a picture in your camera. You have two sizes of paper for your printer: 4 × 6 and 5 × 7. Does it matter? Will the pictures printed from each size of paper be similar?
4 × 6
Sides not proportional, figures not similar.
5 × 7
May 31, 2018
Geometry 8.3 Similar Polygons

29. Geometry 8.3 Similar Polygons
Problem 5
MNOP has a perimeter of 24. Find the perimeter of QRST if MN = 8 and QR = 12.
May 31, 2018
Geometry 8.3 Similar Polygons

30. Geometry 8.3 Similar Polygons
Summary
Two polygons are similar if they have the same shape, but a different size.
If polygons are similar corresponding angles are congruent, and corresponding sides are proportional.
The ratio of any two corresponding sides is the scale factor.
The ratio of the perimeters is equal to the ratio of two corresponding sides.
May 31, 2018
Geometry 8.3 Similar Polygons