Name Date. In Exercises 1 and 2, find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement.

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1 Name ate. ractice In Eercises 1 and, find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement In Eercises 3, cop the diagram. Then use a compass and straightedge to construct a dilation of quadrilateral with the given center and scale factor k. 3. enter, k = 3. enter, k = 1. enter, k = 7% In Eercises 6 and 7, graph the polgon and its image after a dilation with a scale factor k. 1,,,,,, S 1, 3 ; k = 6. ( ) ( ) ( ) ( ),,, 6, 1, 1,, ; k = 7% 7. ( ) ( ) ( ) ( ). standard piece of paper is. inches b 11 inches. piece of legal-size paper is. inches b 1 inches. what scale factor k would ou need to dilate the standard paper so that ou could fit two pages on a single piece of legal paper? 9. The old film-stle cameras created photos that were best printed at 3. inches b inches. Toda s new digital cameras create photos that are best printed at inches b 6 inches. Neither size picture will scale perfectl to fit in an 11-inch b 1-inch frame. Which tpe of camera will ou minimize the loss of the edges of our picture? 10. Your friend claims that if ou dilate a rectangle b a certain scale factor, then the area of the object also increases or decreases b the same amount. Is our friend correct? Eplain our reasoning. 1 in.. in. 11. Would it make sense to state dilation has a scale factor of 1? Eplain our reasoning. opright ig Ideas Learning, LL ll rights reserved. Geometr esources b hapter 131

2 Name ate.6 ractice In Eercises 1 and, graph with vertices ( 1, ), (, 3 ), and (, 1) and its image after the similarit transformation. 1. otation: 10 about the origin. ilation: (, ) ( 1, 1 ) ilation: (, ) (, ) eflection: in the -ais 3. escribe a similarit transformation that maps the black preimage onto the dashed image. X W W X Y Z Z Y In Eercises and, determine whether the polgons with the given vertices are similar. Use transformations to eplain our reasoning.. (, ), (, ), ( 1, ) and. J( ) K( ) L( ) M( ) ( 3, 3 ), E( 3, 1 ), F(, 1) T( 3, 3, ) U(, 3, ) V(,, ) W( 3, 1), 3, 3, 1, 3,,, and 6. rove that the figures are similar. Given Equilateral GHI with side length a, rove equilateral with side length b GHI is similar to. I G a H b 7. Your friend claims ou can use a similarit transformation to turn a square into a rectangle. Is our friend correct? Eplain our answer.. Is the composition of a dilation and a translation commutative? In other words, do ou obtain the same image regardless of the order in which the transformations are performed? Justif our answer. 9. The image shown is known as a Sierpinski triangle. It is a common mathematical construct in the area of fractals. What can ou sa about the similarit transformations used to create the white triangles in this image? 136 Geometr opright ig Ideas Learning, LL esources b hapter ll rights reserved.

3 Name ate.1 ractice In Eercises 1 and, find the scale factor. Then list all pairs of congruent angles and write the ratios of the corresponding side lengths in a statement of proportionalit. 1. LMN S. EFGH L M 13 6 N F 3.6. G 3 E H 1 S 10 In Eercises 3 and, the polgons are similar. Find the value of. 3. U 9 V S T 6 W In Eercises 11, XYZ.. Find the scale factor of to XYZ. 6. Find m X. 7. Find.. Find the area of. Then find the area of XYZ. 9. Find the ratio of the area of to the area of XYZ Z Find and YZ. Eplain our reasoning. 11. Find the ratio of the perimeter of to the perimeter of XYZ. Y W 1 X 1. You are building a roof on a garage such that the gable of the house is similar to the gable of the garage as shown in the diagram. The area of the gable on the house is 30 square feet. Find the area of the gable on the garage. ft House gable 1 ft Garage gable 6 Geometr opright ig Ideas Learning, LL esources b hapter ll rights reserved.

4 nswers. uzzle Time OLYGON. Start Thinking es; The ratio of the distance of the flashlight from the wall and the diameter of the circle remains constant. s the flashlight moves closer to the wall, the circle gets smaller.. Warm Up 1. units. units. umulative eview Warm Up the old film-stle camera 10. no; Ever dimension would dilate b the same scale factor k, so the area would increase b k, one factor of k for each dimension. 11. no; scale factor of 1 does not dilate the object at all. The object is neither enlarged nor reduced.. ractice 1. 1 ; reduction. 1.; enlargement ractice 1. 3; enlargement..; reduction 3..,,.. J J K K L M L M 6. Y Z X V W W 1 V X Z. 6., S S 1 Y 7. It would look like it is 0 millimeters across.. dilation with a scale factor of k = 0 would send all the vertices to the center of the dilation, so the object would be reduced to a point. Geometr nswers opright ig Ideas Learning, LL ll rights reserved.

5 nswers 9. es; The perimeter is additive, so it is scaled b the same factor b which the object is dilated. 10. The scale factor is ; =. Enrichment and Etension 1.. The length and width double; The perimeter doubles; The area increases b a factor of. 3. The perimeter is times as large, and the area is 16 times as large.. The perimeter increases b a factor of a, and the area increases b a factor of a.. (, ) (, ) mm. uzzle Time THE OUTSIE 1. oints,,, and. oints,, and 3. oints, E, F, and G Start Thinking Sample answer: H G E F Length Width erimeter rea square : (1, 1), (1, 1), ( 1 1), ( 1, 1), square EFGH: E(3, 3), F(3, 3), G( 3 3), H( 3, 3); To find square EFGH, use a scale factor of 3, with the origin as the center of the dilation..6 Warm Up 1. n = 9.. w = 1 3. =.. = 13.. c = 1 6. n = 3.6 umulative eview Warm Up 1. inductive reasoning; pattern is used to reach the conclusion.. deductive reasoning; Facts about numbers and the laws of logic are used to reach the conclusion. 3. deductive reasoning; The laws of logic are used to reach the conclusion..6 ractice reflection in the -ais, followed b a dilation with a scale factor of. es; The triangle is a translation; (, ) ( +, 1) followed b a dilation of ( ) (, ), ; oints and F do not follow 3 3 these transformations, so it is not a similarit transformation.. es; The quadrilateral can first be rotated 10 about the origin (or, reflected in the -ais and then the -ais). Then the figure can be dilated with a scale factor of k = 0. and translated to its final position. 6. otate Δ so that side a is parallel to side b. Translate Δ GHI so that point G maps to point. ecause translations preserve angle measure, and all of the angles of an equilateral triangle are 60, Δ GHI lies on Δ. ecause, GI coincides with and GH coincides with, GI lies on and GH lies on. Finall, dilate Δ about point b a scale factor of b so that it is the same a size as Δ GHI. ecause a similarit transformation maps Δ onto Δ GHI, the triangles are similar. 6 opright ig Ideas Learning, LL ll rights reserved. Geometr nswers 3

6 nswers 7. no; square and a rectangle are not similar, so ou cannot use a similarit transformation to change the shape of the object.. no; For eample begin with a unit square centered at the origin. If ou perform a dilation centered at the origin with a scale factor and then translate 1 unit right, the result is not the same as if ou first translate the square 1 unit right and then perform a dilation centered at the origin with a scale factor of. 9. ll white triangles are dilations and translations. There are no rotations in the image.. no; The edges are distorted and curved, and are not an eact replica of the original tet. So, a magnifing glass does not produce a perfect similarit transformation because the image is distorted. 9. no; Similar triangles do not need to be the same size, so there are more similar triangles than there are congruent triangles..6 Enrichment and Etension 1. 1 square units. 3. square units. 6 square units.6 ractice 1.. E E E E E E 1. The area has increased b a factor of = a. k = 3, a = 1, b = 3 3 b. ecause k is 3, the radius of ircle is 3 times the radius of ircle, so t = 3. r.6 uzzle Time THE TEHE TOL THEM NOT TO USE TLES umulative eview a 10 rotation followed b a dilation with a scale factor of 3. similar; The transformation is a translation 6 units to the right and 3 units up, followed b a dilation with a scale factor.. not similar; The transformation is a reflection in the -ais, followed b a translation, however two vertices were translated units up and two vertices were translated 3 units up. 6. otate ΔE onto Δ such that E coincides with. ecause rotations preserve length and measure, E and E is still parallel to. So, coincides with and E coincides with. ilate E coincides with. Therefore, similar to Δ. Δ E until Δ E is 7. no; ircles of different size are simpl a dilation of each other, so the remain similar = 3 1. = = = = = 19. = = 1. = 3. = 3. =. = 3. = 0 6. = 7. =. = 1 9. a. $9.3 b. $ a. fluid ounces b. 6 cups c. 3 pints d. 1. quarts Geometr nswers opright ig Ideas Learning, LL ll rights reserved.

7 nswers 9. FE 0. FE 1. FE. EG 3. FG. 11.; erpendicular isector Theorem (Thm. 6.1). 1.9; onverse of the erpendicular isector Theorem (Thm. 6.) 6. 36; onverse of the erpendicular isector Theorem (Thm. 6.) 7. ; erpendicular isector Theorem (Thm. 6.1). a. 3 b. 36 units c. 7 units hapter.1 Start Thinking Sample answer: The three diagrams are the same image, but stretched or shrunk into different sizes or forms; The first resizing is not similar to the original in a geometric sense. The proportions of the map were not maintained. The second resizing is similar to the original in a geometric sense. It appears to be a dilation of the original in a geometric sense. It appears to be a dilation of the original b a factor less than one and maintains proportionall with the original..1 Warm Up 1. 3 =. = 0 3. = ± = =.1 umulative eview Warm Up 3 =, = ; , 39; the SS ongruence Theorem (Thm..), and XWZ YWZ. ecause corresponding parts of congruent triangles are congruent, = 13 and YZ = ractice 336 ft 1. 3 ; H, I, J, = = HI IJ JH. 3 ; W S, X T, Y U, Z V, WX XY YZ ZW = = = ST TU UV VS in ft 7. a. 7 b. 7. c. 10 d. about 7. units e. about square units f. es; ecause corresponding angles of similar triangles are congruent,. the corresponding ngles onverse Theorem (Thm. 3.), E..1 Enrichment and Etension 1. Sample answer: ractice 1. 3; L, M, N S, LM MN NL = = S S. Sample answer:. ; E, F, G, H, = = = EF FG GH HE opright ig Ideas Learning, LL ll rights reserved. Geometr nswers