1. Similar Polygons & Scale Factor

2. Similarity Ratio
A similarity ratio is the ratio of the lengths of the corresponding sides of two similar polygons.

3. Similar Polygons 1. Corresponding angles are congruent
2. Corresponding sides are proportional

4. Similar Polygons
Have the same shape but not necessarily the same size.
*Same size and shape is congruent.

5. Similarity Statement
ABC ~ DEF

6. Name the pairs of congruent angles.
Exercise 1
Name the pairs of congruent angles.
A 
B 
C 

7. Write the corresponding side lengths in the proportion.
Exercise 2
Write the corresponding side lengths in the proportion.
𝑨𝑩 = 𝑫𝑬 = 𝑭𝑫

8. Circle the correct similarity statement.
Exercise 3
Circle the correct similarity statement.
QRS ~ KJL
RSQ ~ KJL
QSR ~ LKJ

9. Write the corresponding side lengths in the proportion.
Exercise 4
Write the corresponding side lengths in the proportion.
𝑹𝑺 = 𝑲𝑳 =

10. Exercise 5
Substitute numbers for the side lengths and reduce each ratio to simplest form.
𝑫𝑮 𝑴𝑵 =
𝑫𝑬 𝑳𝑴 = =

11. Exercise 6
ABCD ~ EFGH. Solve for x. A B C D 6 x E F G H 18 27

12. Exercise 7
Solve for x and y. A B C S L T x
5 cm
24 cm
10 cm
13 cm y

13. Word problem: A tree cast a shadow 18 feet long
Word problem: A tree cast a shadow 18 feet long. At the same time a person who is 6 feet tall cast a shadow 4 feet long. How tall is the tree?

14. Ratio of Similar Polygons
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Ratio of Similar Polygons
Corresponding Sides : Corresponding Sides Or
Perimeter : Perimeter
A : B

15. Ratio of Similar Polygons
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Ratio of Similar Polygons
Area : Area
A2 : B2

16. Ratio of Similar Polygons
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Ratio of Similar Polygons
Volume: Volume
A3 : B3

17. Find the perimeter of the smaller triangle.
12 cm
4 cm
Perimeter = 60 cm
Perimeter = x
x = 20 cm

18. The ratio of the perimeters of two similar polygons equals the ratio of any pair of corresponding sides.
The ratio of the perimeters of CAT to DOG is 3:2
Find the value of y. A
C T O
D G 4 10 y
y = 4

19. Scale Factor – the ratio of a new image to its original image
The ratio of corresponding sides

20. Scale Factor
When scale factor is greater than 1, the shape gets bigger (enlargement).
When scale factor is less than 1, but greater than 0, the shape gets smaller (reduction).

21. new SCALE FACTOR. 𝐹𝑜𝑟𝑚𝑢𝑙𝑎: 𝑛𝑒𝑤 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 new original 6 2 7 14 10 5 3 6
𝐹𝑜𝑟𝑚𝑢𝑙𝑎: 𝑛𝑒𝑤 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙

22. Dilations 𝐷 𝑥,𝑦 → 1 2 𝑥, 1 2 𝑦 𝐴 4,10 , 𝐵 −6,4 , 𝑎𝑛𝑑 𝐶(4,−4)
Apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points. Identify and describe the transformation as an enlargement or reduction.
𝐷 𝑥,𝑦 → 1 2 𝑥, 1 2 𝑦
𝐴 4,10 , 𝐵 −6,4 , 𝑎𝑛𝑑 𝐶(4,−4)
𝐴′ , , 𝐵′ , ,
𝑎𝑛𝑑 𝐶′( , )
This shape is a/n __________________________.
The scale factor is _________.

23. Dilations 𝐷 𝑥,𝑦 → 3𝑥, 3𝑦 𝑃 1,−1 , 𝑄 2,1 , 𝑎𝑛𝑑 𝑅(−2,1) 𝑃′ , , 𝑄′ , ,
Apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points. Identify and describe the transformation as an enlargement or reduction.
𝐷 𝑥,𝑦 → 3𝑥, 3𝑦
𝑃 1,−1 , 𝑄 2,1 , 𝑎𝑛𝑑 𝑅(−2,1)
𝑃′ , , 𝑄′ , ,
𝑎𝑛𝑑 𝑅′( , )
This shape is a/n __________________________.
The scale factor is _________.

24. Worksheet