STUDY GUIDE REVIEW Similarity and Transformations. 8 y

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1 MODUL Study Guide Review SSSSMNT ND INTRVNTION ssign or customize module reviews. STUDY GUID RVIW Similarity and Transformations ssential Question: How can you use similarity and transformations to solve real-world problems? KY XMPL (Lesson.1) Determine the center of dilation and the scale factor of the dilation. 8 y 6 2 O x MODUL Key Vocabulary center of dilation (centro de dilatación) dilation (dilatación) scale factor (factor de escala) Side-Side-Side Similarity (Similitud Lado -Lado -Lado) Side-ngle-Side Similarity (Similitud Lado-Ángulo- Lado) similar (semejantes) similarity transformation (transformación de semejanza) Draw a line through and. Draw a line through and. Draw a line through and. The three lines intersect at point O (2, 3). Find the distance from point O to points and '. d = (2-3) 2 + (3 - ) 2 = _ 2 Find the distance to point. d = (2 - ) 2 + (3-5) 2 = 2 _ 2 Find the distance to point '. The distance from point O to point is twice the distance from point O to point. The scale factor of dilation is 2 to 1. KY XMPL (Lesson.3) D maps to FGH by a similarity transformation. Write a proportion that contains and H. Then list any angles that are congruent to D or. orresponding sides of similar figures are proportional. FG and H D, so _ FG = D_ H. orresponding angles of similar figures are congruent. D H and. Module 623 Study Guide Review 623 Module

2 KY XMPL (Lesson.) Determine whether and DF are similar. If so, justify by SSS Similarity or SS Similarity D F heck that the ratios of the lengths of corresponding sides are equal = = 3 Since all the ratios of the lengths of corresponding sides are equal, the triangles are similar by SSS Similarity. XRISS Determine the following for the dilation. (Lesson.1) 8 y 6 D 2 D x 0 2 O 6 8 (3, 0) 1. center 2. scale factor 1 to 3 Module 62 Study Guide Review Study Guide Review 62

3 MODUL PRFORMN TSK OMMON OR Mathematical Practices: MP.1, MP.2, MP., MP.6 G-MG..1, G-MG..3 SUPPORTING STUDNT RSONING Students should begin this problem by focusing on what information they will need. Here are some issues they might bring up. What should be the maximum height of the model: Students can either work backwards from the desired height or find a percent of the actual height and use it to determine the scale. Which dimensions are not needed for a scale model: Students can decide which dimensions might not be needed, such as the height at which the stone color changes. How to determine the dimensions of the model: Students should use proportions to convert the actual dimensions to the scaled dimensions. Students may first want to convert the actual dimensions to decimals. What materials should be used: Students can research the appropriate materials to use or you can make suggestions. Determine whether the two figures are similar using similarity transformations. (Lesson.2) 3. to DF similar. D to FGH 8 y x D F not similar D F 13 2 D - F 0 2 maps to DF by a similarity transformation. (Lesson.3) 5. Write a proportion that contains and F. 6. Write a proportion that contains and DF. 7. List any angles that are congruent to or. D = F Determine whether and DF are similar. If so, justify by SSS or SS. (Lesson.) F = DF 6-2 D; SS y not similar x G H D F Module 625 Study Guide Review SFFOLDING SUPPORT Students should recognize that they will need to convert units of the given measurements so that all units are the same. Possible units are feet, inches, meters, or centimeters. If students choose to solve the problem by first deciding on a scale factor, they will need to make sure the scale factor they use results in a model which will fit inside a classroom. 625 Module

4 MODUL PRFORMN TSK Designing a Model of the Washington Monument Your challenge is to design a scale model of the Washington Monument that would be small enough to fit inside your classroom. Here are some key dimensions of the Washington Monument for you to consider in determining the scale factor for your model. (Note that the color of the stone changes part way up the monument because of a halt in construction between 185 and 1877.) Total height Key Dimension Height to top of trapezoidal side Width at base Width at top of trapezoidal side Height at which stone color changes Measurement 555 ft 5 in. 500 ft 55 ft 1 in. 3 ft 5 in. 151 ft What scale factor will you use for your model? What are the key dimensions of your model? egin by making some notes in the space below about your strategy for designing the model. Then use your own paper to complete the task. Present your plan using diagrams, words, and/or numbers. Image redits: lzzy Schwartz/Digital Vision/Getty Images SMPL SOLUTION Use the scale 1 in. = 10 ft. First, convert units so that all measurements are in 1 ft feet, by multiplying inches by the ratio _ 12 in. and adding that to the number of feet. The results are: Total height: ft Width at base: ft Width at top of trapezoidal side: 3.2 ft To find the model s dimensions, solve the proportion: 1 in. 10 ft = model height actual height Using the proportion, check the total height of the model to see if it will fit inside the classroom. 1 in. 10 ft = x x 55.5 in ft 1 ft This is 55.5 ( 12 in.).6 ft tall, so the scale factor is reasonable. The remaining dimensions are as follows. Height to top of trapezoidal side: 50 in. Width at base: 5.5 in. Width at top of trapezoidal side: 3. in. MODUL Height at which stone color changes: 15.1 in. Module 626 Study Guide Review DISUSSION OPPORTUNITIS If students choose to work backwards from a desired height of exactly six feet, how will this change the calculations and scale factor used? What are some advantages to choosing a scale that makes the model no more than a foot tall? Sample answer: The amount of material needed to construct the model will be much less, which in turn will lower both the cost and the weight and make the model more portable. ssessment Rubric 2 points: Student correctly solves the problem and explains his/her reasoning. 1 point: Student shows good understanding of the problem but does not fully solve or explain. 0 points: Student does not demonstrate understanding of the problem. Study Guide Review 626

5 Ready to Go On? SSSS MSTRY Use the assessment on this page to determine if students have mastered the concepts and standards covered in this module. SSSSMNT ND INTRVNTION ccess Ready to Go On? assessment online, and receive instant scoring, feedback, and customized intervention or enrichment. Ready to Go On?.1. Similarity and Transformations nswer each problem about the image. (Lesson.1) 1. re the two shapes similar? 2. Find the scale factor k. 3. Find the center of dilation.. ompare k to the ratio area D area D. Determine which of the following transformations are dilations. (Lesson.1) 5. (x, y) (x, y) 6. (x, y) (-x, 3y) Dilation 7. (x, y) (x - 2, y - 2) 8. (x, y) ( 1_ 3 x, 1_ 3 y ) Not a dilation 3 Yes (, 2) Th e ratio equals 9, which is the square of the scale factor. Not a dilation Dilation 16 y 12 8 Online Homework Hints and Help xtra Practice D D x DDITIONL RSOURS Response to Intervention Resources Reteach Worksheets Differentiated Instruction Resources Reading Strategies Success for nglish Learners hallenge Worksheets ssessment Resources Leveled Module Quizzes Find the missing length. (Lesson.3) 9. XYZ maps to MNO with the transformation (x, y) (7x, 7y). If XY = 3, what is the length of MN? 21 Find the appropriate statements about the triangles. (Lesson.) 10. is similar to RTS. Write a proportion that contains and RT. lso write the angle congruence statements that must be true. RS = _, R, T, S RT SSNTIL QUSTION. How can you determine whether a shape is similar to another shape? nswers may vary. Sample: Two shapes are similar only if one shape can be mapped to the other through similarity transformations. These transformations are the rigid motions, meaning reflections, translations, and rotations, as well as dilations. Module 627 Study Guide Review OMMON OR ommon ore Standards Lesson Items ontent Standards Mathematical Practices.2 1 G-SRT..2, G-SRT..1b, G-O..2 MP G-SRT..1b MP G-SRT..1b, G-O..2 MP G-SRT..1b, G-O..2 MP G-SRT..2 MP. 627 Module

6 MODUL MIXD RVIW ssessment Readiness 1. onsider each transformation. Does the transformation preserve distance? Select Yes or No for.. Dilations Yes No. Reflections Yes No. Rotations Yes No 2. MNO maps to RST with the transformation (x, y) 1_ ( 3 x, 1_ 3 y ). hoose True or False for each statement.. If RT = 3, MO = 9. True False. If RT = 12, MO =. True False. If RT = 9, MO = 27. True False 3. Determine if the following pair of triangles are similar. If so, explain how. Note that D. Possible nswer: and D are congruent because they are alternate interior angles. and D are congruent because it is given they have the same measure. So the two triangles are similar by ngle ngle Similarity D MIXD RVIW ssessment Readiness SSSSMNT ND INTRVNTION ssign ready-made or customized practice tests to prepare students for high-stakes tests. DDITIONL RSOURS MODUL ssessment Resources Leveled Module Quizzes: Modified,. If is similar to XYZ and YZX, what special type of triangle is? Justify your reasoning. nswers may vary. Sample: xamine the corresponding angles. Since is similar to XYZ, this means X. Likewise, since is similar to YZX, this means Y. Thus, by the Transitive Property of ongruence, it can be said that X Y. lso, Y and Z, which means Y Z by the Transitive Property of ongruence. Putting these facts together, it can be shown that X Y Z. Therefore, XYZ, YZX, and by similarity, are all equilateral triangles. VOID OMMON RRORS Item 2 Some students have trouble following a dilation rule backward. Remind students that if moving from the image to the original figure, multiply by the reciprocal of the original dilation. Module 628 Study Guide Review OMMON OR ommon ore Standards Lesson Items ontent Standards Mathematical Practices.1, 1.3 1* G-SRT..2 MP G-SRT..1 MP.7. 3 G-SRT..3 MP.7.3, 7.2 * G-SRT..2 MP.3 * Item integrates mixed review concepts from previous modules or a previous course. Study Guide Review 628