Similarity Transformation LESSON 7–6 Similarity Transformation

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

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

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

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

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

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

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

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

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

Concept

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Similarity Transformation LESSON 7–6 Similarity Transformation