1. Similarity Transformation LESSON 7–6

2. Lesson Menu 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

3. Over Lesson 7–5 5-Minute Check 1 A.1 B.2 C.3.5 D.5 Find the value of a.

4. Over Lesson 7–5 5-Minute Check 2 A.45 B.54 C.67 D.76 The triangles are similar. Find the value of n.

5. Over Lesson 7–5 5-Minute Check 3 A.8.5 B.9 C.10 D.11 Find the value of x.

6. Over Lesson 7–5 5-Minute Check 4 A.9 B.10 C.11 D.12 Find the value of x.

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

8. TEKS 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)

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

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

11. Concept

12. Example 1 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.

13. Example 1 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 2 4

14. Example 1 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.

15. Example 1 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

16. Example 1 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 1 2

17. Example 1 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 3 3 2

18. Example 2 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.

19. Example 2 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 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?

20. Example 3 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.

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

22. Example 3 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)

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

24. Example 3 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 1 3 3 2 3 4

25. Example 3 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

26. Similarity Transformation LESSON 7–6