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Five-Minute Check (over Lesson 7–5) CCSS 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 Practices 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.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Mathematical Practices 6 Attend to precision. 4 Model with mathematics. CCSS

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: M(–6, –3), N(6, –3), O(–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: M(–6, –3), N(6, –3), O(–6, 6) image: D(–2, –1), F(2, –1), G(–2, 2) Graph each figure. Since M and D are both right angles, M  D. Show that the lengths of the sides that include M and D are proportional. Example 3

Verify Similarity after a Dilation Use the coordinate grid to find the lengths of the vertical segments MO and DG and the horizontal segments MN and DF. Answer: Since the lengths of the sides that include M and D are proportional, ΔMNO ~ ΔDFG by SAS Similarity. Example 3

original: G(2, 1), H(4, 1), I(2, 0), J(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: G(2, 1), H(4, 1), I(2, 0), J(4, 0) image: Q(4, 2), R(8, 2), S(4, 0), T(8, 0) Example 3

Find and compare the ratios of corresponding sides. Verify Similarity after a Dilation Since the figures are rectangles, their corresponding angles are congruent. Find and compare the ratios of corresponding sides. Answer: 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

End of the Lesson