1. Five-Minute Check (over Lesson 7–1) Mathematical Practices Then/Now
New Vocabulary
Example 1: Determine Whether Polygons Are Similar
Key Concept: Similar Polygons
Example 2: Use a Similarity Statement
Example 3: Real-World Example: Identify Similar Polygons
Example 4: Use Similar Figures to Find Missing Measures
Key Concept: Properties of Similarity
Theorem 7.1: Perimeters of Similar Polygons
Example 5: Use a Scale Factor to Find Perimeter
Lesson Menu

2. There are 480 sophomores and 520 juniors in a high school
There are 480 sophomores and 520 juniors in a high school. Find the ratio of juniors to sophomores.
A. 10:8
B. 13:12
C. 19:17
D. 22:20
5-Minute Check 1

3. A strip of wood molding that is 33 inches long is cut into two pieces whose lengths are in the ratio of 7:4. What are the lengths of the two pieces?
A. 7 in., 4 in.
B. 14 in., 8 in.
C. 18 in., 15 in.
D. 21 in., 12 in.
5-Minute Check 2

4. A. 7
B. 8
C. 9
D. 10
5-Minute Check 3

5. A. 2.75
B. 3.25
C. 3.75
D. 4.25
5-Minute Check 4

6. A. 4
B. 3
C. 2
D. 1
5-Minute Check 5

7. The standard ratio of a photo’s width to its length is
The standard ratio of a photo’s width to its length is What is the length of a photo that has a width of 14 inches?
A. 9.3 inches
B. 17 inches
C. 20 inches
D. 56 inches
5-Minute Check 6

8. Mathematical Practices
1 Make sense of problems and persevere in solving them.
6 Attend to precision.
Content Standards
G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
G. SRT. 3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. MP

9. You drew the image of a figure after a dilation.
Use the definition of similarity to identify similar polygons.
Solve problems by using the properties of similar polygons.
Then/Now

10. similar polygons
similarity
transformation
scale factor
New Vocabulary

11. Determine whether the given polygons are similar. Explain.
Determine Whether Polygons Are Similar
Determine whether the given polygons are similar.
Explain.
A. ABCD and EFGH
Example 1A

12. Are the polygons the same shape? Yes
Determine Whether Polygons Are Similar
Are the polygons the same shape?
Yes
Will a transformation map one polygon to the other?
Yes
Is one polygon a scale of the other?
Yes
Yes
Are the polygons similar?
Answer: Yes; map ABCD to EFGH using a dilation centered at the origin with scale factor followed by a translation along [– 2, 4].
Example 1A

13. Determine whether the given polygons are similar. Explain.
Determine Whether Polygons Are Similar
Determine whether the given polygons are similar.
Explain.
B. PQR and STU
Example 1B

14. Are the triangles the same shape? No
Determine Whether Polygons Are Similar
Are the triangles the same shape? No
Will a transformation map one triangle to the other? No
Are the triangles similar? No
Answer: No; the triangles do not have the same shape, so there are no similarity transformations that will map one to the other.
Example 1B

15. Key Concept

16. List the congruent angle pairs.
Use a Similarity Statement
If ABC ∼ RST, list all pairs of congruent angles and write a proportion that relates the corresponding sides.
List the congruent angle pairs.
A ≅ R, B ≅ S, C ≅ T
Example 2

17. List the corresponding similar sides.
Use a Similarity Statement
List the corresponding similar sides.
AB ~ RS, BC ~ ST, AC ~ RT
Write a proportion that relates to the corresponding sides.
Answer:
Example 2

18. Menus Tan is designing a new menu for the
Identify Similar Polygons
Menus Tan is designing a new menu for the
restaurant where he works. Determine whether
the following sizes for the new menu are similar
to the original menu. If so, write the similarity
statement and scale factor. Explain your reasoning.
Real-World Example 3

19. Write a proportion that relates to the corresponding sides.
Identify Similar Polygons A.
Write a proportion that relates to the corresponding sides.
Real-World Example 3A

20. Substitute the lengths of the sides.
Identify Similar Polygons
Substitute the lengths of the sides.
Simplify.
Are the fractions equal? No
The menus are not similar because the sides are not proportional.
Answer:
Real-World Example 3A

21. Write a proportion that relates to the corresponding sides.
Identify Similar Polygons B.
Write a proportion that relates to the corresponding sides.
Real-World Example 3B

22. Substitute the lengths of the sides.
Identify Similar Polygons
Substitute the lengths of the sides.
Simplify.
Are the fractions equal?
Yes
The menus are similar because the sides are proportional.
Answer:
Real-World Example 3B

23. The two polygons are similar.
Use Similar Figures to Find Missing Measures
The two polygons are similar.
A. Find x.
Example 4A

24. Write a proportion that relates to the corresponding sides.
Use Similar Figures to Find Missing Measures
Write a proportion that relates to the corresponding sides.
Substitute the lengths of the sides.
Solve for x.
Answer:
Example 4A

25. The two polygons are similar.
Use Similar Figures to Find Missing Measures
The two polygons are similar.
B. Find y.
Example 4B

26. Answer: Write a proportion that relates to the corresponding sides.
Use Similar Figures to Find Missing Measures
Write a proportion that relates to the corresponding sides.
Substitute the lengths of the sides.
Solve for y
Answer:
Example 4B

27. Key Concept

28. Theorem

29. Use a Scale Factor to Find Perimeter
If ABCDE ∼ RSTUV, find the scale factor of from RSTUV to ABCDE and the perimeter of each polygon.
Example 5

30. List the corresponding similar sides.
Use a Scale Factor to Find Perimeter
List the corresponding similar sides.
AB ~ RS, BC ~ ST, CD ~ TU, DE ~ UV, AE ~ VR
Write a proportion that relates to the corresponding sides.
Find the lengths of the missing side ST.
Example 5

31. Find the lengths of the missing side DC.
Use a Scale Factor to Find Perimeter
Solve for y.
Find the lengths of the missing side DC.
Solve for x.
Example 5

32. Find the perimeter of each polygon:
Use a Scale Factor to Find Perimeter
Find the perimeter of each polygon:
ABCDE = = 26
RSTUV = = 45.5
Answer: scale factor: perimeter of ABCDE: 26; perimeter of RSTUV: 45.5
Example 5