DO NOW Geometry Regents Lomac Date. due. Similar by Transformation 6.1 J'' J''' J'''

Transcription

1 DO NOW Gomtry Rgnts Lomac Dat. du. Similar by Transformation 6.1 (DN) Nam th thr rigid transformations and sktch an xampl that illustrats ach on. Nam Pr LO: I can dscrib a similarity transformation, which is a squnc of rigid motions and dilations, that will map on shap to anothr or xplain why it is not possibl. (1) Similarity: Mapping on figur to anothr through a composition of transformations. (a) Obsrv th figurs J, J''', and th intrmdiat imags btwn J and J''' blow. J and J''' ar similar. Dscrib transformations that will map on figur to th nxt. Whr ndd, add points and lins to th diagram, approximat angl masurs and us a rulr to stimat scal factors. J J'' J' J J' J' J'' J'' J''' J''' (b) From part (a), thr is a squnc of transformations that will map J to J'''. Writ th squnc in short notation blow. (c) Rad th critrion similar figurs blow. ( ( ( ))) * Two figurs ar similar if thr xists a similarity transformation that maps on figur onto th othr. * A similarity transformation is a composition of a finit numbr of dilations, translations, rflctions, and/or rotations of th plan. Basd on th dfinition you just rad, is figur J similar to J'''? Dscrib you how know.

2 6.1 (2) Similarity: Mapping on figur to anothr through a composition of transformations. (a) Damian usd a diffrnt squnc of transformations to map J to J'''. Dos his procss also work? If so, writ a composition of similarity transformations that will map J to J'''. J J' J'' J''' ( ( ( ))) (b) So far, you hav dscribd two squncs of transformations that will map J to J'''. Us th diagram blow to writ your own squnc of transformations that is diffrnt from th two you hav alrady sn. Sktch your squnc of transformations and writ it in short notation blow. J J''' ( ( ( )))

3 (3) Similarity: Mapping on figur to anothr through a composition of transformations. (a) Figur S is similar to figur S''. Which transformations compos th similarity transformation that maps S onto S''? S' 6.1 S S'' Writ th squnc in notation: (b) Figur P is similar to figur P''. Which transformations compos th similarity transformation that maps P onto P''? P' P'' P Figur P is not ONLY similar to figur P'', it is also to P''. is a spcial cas of similarity whn th scal factor for dilation would b. Writ th squnc in short notation: (c) Show that no squnc of basic rigid motions and dilations taks th small figur to th larg figur. Tak masurmnts as ndd.

4 6.1 (4) Similarity: Mapping on figur to anothr through a composition of transformations. Dscrib th rlationship btwn scal drawings, dilations, and similar figurs by rsponding to th prompts blow. (1) How ar scal drawings and dilations alik? (2) How ar scal drawings and dilations diffrnt? (1) What is th rlationship of similar figurs to scal drawings and dilations? (5) Is thr a squnc of basic rigid motions and dilations taks th larg figur to th small figur. Tak masurmnts as ndd. If thr is on, writ th squnc in short notation:

5 6.1 (4) Similarity: Mapping on figur to anothr through a composition of transformations. Construct a squnc of basic rigid motions and dilations taks figur A to figur B. Tak masurmnts as ndd. Writ th squnc in short notation:

6 (5) Exit Tickt (1) Givn th diagram blow, idntify a similarity transformation, if on xists, that maps G onto H. If on dos not xist, xplain why. Provid any ncssary masurmnts to justify your answr. 6.1 (6) Homwork (1) Givn th coordinat plan shown, idntify a similarity transformation, if on xists, mapping X onto Y. If on dos not xist, xplain why. (2) Tddy corrctly idntifid a similarity transformation with at last on dilation that maps Figur I onto Figur II bgan corrctly idntifid a congrunc transformation that maps Figur I onto Figur II. What must b tru about Tddy s similarity transformation?

7 (6) cont. Homwork (3) Givn th coordinat plan shown, idntify a similarity transformation, if on xists, that maps ABCD onto A'''B'''C'''D'''. If on dos not xist, xplain why. 6.1 (4) Th diagram blow shows a dilation of th plan... or dos it? Explain your answr.