1. Similarity Transformation
LESSON 7–6
Similarity Transformation

2. Five-Minute Check (over Lesson 7–5) TEKS Then/Now New Vocabulary
Concept Summary: Types of Dilations
Example 1: Identify a Dilation and Find Its Scale Factor
Example 2: Real-World Example: Find and Use a Scale Factor
Example 3: Verify Similarity after a Dilation
Lesson Menu

3. Find the value of a.
A. 1
B. 2
C. 3.5
D. 5
5-Minute Check 1

4. The triangles are similar. Find the value of n.
B. 54
C. 67
D. 76
5-Minute Check 2

5. Find the value of x.
A. 8.5
B. 9
C. 10
D. 11
5-Minute Check 3

6. Find the value of x.
A. 9
B. 10
C. 11
D. 12
5-Minute Check 4

7. Find the value of x.
A. 1
B. 4.5
C. 2.6
D. 2.4
5-Minute Check 5

8. Mathematical Processes G.1(E), G.1(G)
Targeted TEKS
G.7(A) Apply the definition of similarity in terms of a dilation to
identify similar figures and their proportional sides and the congruent corresponding angles.
Mathematical Processes
G.1(E), G.1(G)
TEKS

9. You identified congruence transformations.
Identify similarity transformations.
Verify similarity after a similarity transformation.
Then/Now

10. similarity transformation center of dilation
scale factor of a dilation
enlargement
reduction
Vocabulary

11. Concept

12. B is smaller than A, so the dilation is a reduction.
Identify a Dilation and Find Its Scale Factor
A. Determine whether the dilation from Figure A to Figure B is an enlargement or a reduction. Then find the scale factor of the dilation.
B is smaller than A, so the dilation is a reduction.
Example 1

13. Answer: So, the scale factor is or . 1 2 4
Identify a Dilation and Find Its Scale Factor
The distance between the vertices at (2, 2) and (2, –2) for A is 4 and from the vertices at (1, 1) and (1, –1) for B is 2.
Answer: So, the scale factor is or . __ 1 2 4
Example 1

14. B is larger than A, so the dilation is an enlargement.
Identify a Dilation and Find Its Scale Factor
B. Determine whether the dilation from Figure A to Figure B is an enlargement or a reduction. Then find the scale factor of the dilation.
B is larger than A, so the dilation is an enlargement.
Example 1

15. Answer: So, the scale factor is or 3. 6 2
Identify a Dilation and Find Its Scale Factor
The distance between the vertices at (3, 3) and (–3, 3) for A is 6 and from the vertices at (1, 1) and (–1, 1) for B is 2.
Answer: So, the scale factor is or 3. __ 6 2
Example 1

16. A. Determine whether the dilation from Figure A to Figure B is an enlargement or a reduction. Then find the scale factor of the dilation.
A. reduction;
B. reduction;
C. enlargement; 2
D. enlargement; 3 __ 1 3 2
Example 1

17. B. Determine whether the dilation from Figure A to Figure B is an enlargement or a reduction. Then find the scale factor of the dilation.
A. reduction;
B. reduction;
C. enlargement;
D. enlargement; 2 __ 1 3 2
Example 1

18. Answer: The enlarged receipt will be 3 inches by 8 inches.
Find and Use a Scale Factor
PHOTOCOPYING A photocopy of a receipt is 1.5 inches wide and 4 inches long. By what percent should the receipt be enlarged so that its image is 2 times the original? What will be the dimensions of the enlarged image?
To enlarge the receipt 2 times the original, use a scale factor of 2. Written as a percent, the scale factor is (2 ● 100%) or 200%. Now, find the dimensions of the enlarged receipt.
width: 1.5 in. ● 200% = 3 in.
length: 4 in. ● 200% = 8 in.
Answer: The enlarged receipt will be 3 inches by 8 inches.
Example 2

19. PHOTOGRAPHS Mariano wants to enlarge a picture he took that is 4 inches by 7.5 inches. He wants it to fit perfectly into a frame that is 400% of the original size. What will be the dimensions of the enlarged photo?
A. 15 inches by 25 inches
B. 8 inches by 15 inches
C. 12 inches by 22.5 inches
D. 16 inches by 30 inches
Example 2

20. original: A(–6, –3), B(6, –3), C(–6, 6)
Verify Similarity after a Dilation
A. Graph the original figure and its dilated image. Then verify that the dilation is a similarity transformation.
original: A(–6, –3), B(6, –3), C(–6, 6)
image: D(–2, –1), E(2, –1), F(–2, 2)
Graph each figure. Since A and D are both right angles, A  D Show that the lengths of the sides that include A and D are proportional.
Example 3

21. Verify Similarity after a Dilation
Answer: Since the lengths of the sides that include M and D are proportional, ΔMNO ~ ΔDFG by SAS Similarity.
Example 3

22. original: P(2, 1), Q(4, 1), S(2, 0), R(4, 0)
Verify Similarity after a Dilation
B. Graph the original figure and its dilated image. Then verify that the dilation is a similarity transformation.
original: P(2, 1), Q(4, 1), S(2, 0), R(4, 0)
image: W(4, 2), X(8, 2), R(4, 0), T(8, 0)
Example 3

23. Verify Similarity after a Dilation
Since the figures are rectangles, their corresponding angles are congruent.
Example 3

24. A. Graph the original figure and its dilated image
A. Graph the original figure and its dilated image. Then determine the scale factor of the dilation. original: B(–7, –2), A(5, –2), D(–7, 7) image: J(–3, 0), K(1, 0), L(–3, 3) A. B. C. D. __ 1 2 3 4
Example 3

25. B. Graph the original figure and its dilated image
B. Graph the original figure and its dilated image. Then determine the scale factor of the dilation. original: A(4, 3), B(6, 3), C(4, 2), D(6, 2) image: E(6, 4), F(10, 4), G(6, 2), H(10, 2)
A. 2 B.
C. 3
D. 4 __ 1 3
Example 3

26. Similarity Transformation
LESSON 7–6
Similarity Transformation