Two figures are similar fi gures when they have the same shape but not necessarily the same size.

Transcription

1 NDIN O PIION. o be poficient in math, ou need to ue clea definition in dicuion with othe and in ou own eaoning. imilait and anfomation ential uetion When a figue i tanlated, eflected, otated, o dilated in the plane, i the image alwa imila to the oiginal figue? wo figue ae imila fi gue when the have the ame hape but not neceail the ame ize. Dilation and imilait Wok with a patne. a. Ue dnamic geomet oftwae to daw an tiangle and label it. b. Dilate the tiangle uing a cale facto of 3. I the image imila to the oiginal tiangle? Jutif ou anwe D imila iangle ample Point (, 1) ( 1, 1) (1, 0) D(0, 0) egment =. =. = 3.1 ngle m = 5 m = 90 m = 5 igid Motion and imilait Wok with a patne. a. Ue dnamic geomet oftwae to daw an tiangle. b. op the tiangle and tanlate it 3 unit left and unit up. I the image imila to the oiginal tiangle? Jutif ou anwe. c. eflect the tiangle in the -ai. I the image imila to the oiginal tiangle? Jutif ou anwe. d. otate the oiginal tiangle 90 counteclockwie about the oigin. I the image imila to the oiginal tiangle? Jutif ou anwe. ommunicate You nwe 3. When a figue i tanlated, eflected, otated, o dilated in the plane, i the image alwa imila to the oiginal figue? plain ou eaoning.. figue undegoe a compoition of tanfomation, which include tanlation, eflection, otation, and dilation. I the image imila to the oiginal figue? plain ou eaoning. ection. imilait and anfomation 15

2 . Leon What You Will Lean oe Vocabula imilait tanfomation, p. 1 imila figue, p. 1 Pefom imilait tanfomation. Decibe imilait tanfomation. Pove that figue ae imila. Pefoming imilait anfomation dilation i a tanfomation that peeve hape but not ize. o, a dilation i a nonigid motion. imilait tanfomation i a dilation o a compoition of igid motion and dilation. wo geometic figue ae imila figue if and onl if thee i a imilait tanfomation that map one of the figue onto the othe. imila figue have the ame hape but not neceail the ame ize. onguence tanfomation peeve length and angle meaue. When the cale facto of the dilation() i not equal to 1 o 1, imilait tanfomation peeve angle meaue onl. Pefoming a imilait anfomation aph with vetice (, 1), (, ), and (, 1) and it image afte the imilait tanfomation. anlation: (, ) ( + 5, + 1) Dilation: (, ) (, ) OLUION tep 1 aph. 8 (, ) (, ) (, 1) (3, 3) (, ) (, ) (1, ) (3, ) (, 1) 8 tep anlate 5 unit ight and 1 unit up. ha vetice (1, ), (3, 3), and (3, ). tep 3 Dilate uing a cale facto of. ha vetice (, ), (, ), and (, ). Monitoing Poge Help in nglih and panih at igideamath.com 1. aph D with endpoint (, ) and D(, ) and it image afte the imilait tanfomation. otation: 90 about the oigin Dilation: (, ) ( 1, 1 ). aph H with vetice (1, ), (, ), and H(, 0) and it image afte the imilait tanfomation. eflection: in the -ai Dilation: (, ) (1.5, 1.5) 1 hapte anfomation

3 Decibing imilait anfomation Decibing a imilait anfomation Decibe a imilait tanfomation that map tapezoid P to tapezoid WXYZ. P X W Y Z OLUION fall fom left to ight, and XY ie fom left to ight. If ou eflect tapezoid P in the -ai a hown, then the image, tapezoid P, will have the ame oientation a tapezoid WXYZ. P(, 3) ( 3, 3) (3, 3) X P (, 3) W Y Z (, 3) (0, 3) (0, 3) (, 3) apezoid WXYZ appea to be about one-thid a lage a tapezoid P. Dilate tapezoid P uing a cale facto of 1 3. (, ) ( 1 3, 1 3 ) P (, 3) P (, 1) (3, 3) (1, 1) (0, 3) (0, 1) (, 3) (, 1) he vetice of tapezoid P match the vetice of tapezoid WXYZ. o, a imilait tanfomation that map tapezoid P to tapezoid WXYZ i a eflection in the -ai followed b a dilation with a cale facto of 1 3. Monitoing Poge 3. In ample, decibe anothe imilait tanfomation that map tapezoid P to tapezoid WXYZ.. Decibe a imilait tanfomation that map quadilateal D to quadilateal UV. Help in nglih and panih at igideamath.com D U V ection. imilait and anfomation 17

4 Poving igue e imila o pove that two figue ae imila, ou mut pove that a imilait tanfomation map one of the figue onto the othe. Poving hat wo quae e imila Pove that quae D i imila to quae H. iven quae D with ide length, quae H with ide length, D H Pove quae D i imila to quae H. D H OLUION anlate quae D o that point map to point. ecaue tanlation map egment to paallel egment and D H, the image of D lie on H. D H ecaue tanlation peeve length and angle meaue, the image of D, D, i a quae with ide length. ecaue all the inteio angle of a quae ae ight angle, D H. When D coincide with H, coincide with. o, lie on. Net, dilate quae D uing cente of dilation. hooe the cale facto to be the atio of the ide length of H and D, which i. D H hi dilation map D to H and to becaue the image of D and have ide length () = and the egment D and lie on line paing though the cente of dilation. o, the dilation map to and D to H. he image of lie () = unit to the ight of the image of and () = unit above the image of D. o, the image of i. H D H N imilait tanfomation map quae D to quae H. o, quae D i imila to quae H. v Monitoing Poge Help in nglih and panih at igideamath.com t K P M 5. Pove that JKL i imila to MNP. iven ight iocele JKL with leg length t, ight iocele MNP with leg length v, LJ PM L J Pove JKL i imila to MNP. 18 hapte anfomation

5 . ecie Dnamic olution available at igideamath.com Vocabula and oe oncept heck 1. VOULY What i the diffeence between imila fi gue and conguent fi gue?. OMPL H NN tanfomation that poduce a imila figue, uch a a dilation, i called a. Monitoing Poge and Modeling with Mathematic In ecie 3, gaph H with vetice (, ), (, ), and H(, ) and it image afte the imilait tanfomation. (ee ample 1.) 3. anlation: (, ) ( + 3, + 1) Dilation: (, ) (, ). Dilation: (, ) ( 1, 1 ) eflection: in the -ai 5. otation: 90 about the oigin Dilation: (, ) (3, 3). Dilation: (, ) ( 3, 3 ) eflection: in the -ai In ecie 7 and 8, decibe a imilait tanfomation that map the blue peimage to the geen image. (ee ample.) 7. D V U In ecie 9 1, detemine whethe the polgon with the given vetice ae imila. Ue tanfomation to eplain ou eaoning. 9. (, 0), (9, ), (1, ) and D(0, 3), (1, 5), (, 5) 10. ( 1, 0), (, ), (1, 3), (, 1) and W(0, ), X(, ), Y(, ), Z(, ) 11. (, 3), H(, 3), I(, 0) and J(1, 0), K(, ), L(1, ) 1. D(, 3), (, 3), ( 1, 1), (, 1) and L(1, 1), M(3, 1), N(, 3), P(1, 3) In ecie 13 and 1, pove that the figue ae imila. (ee ample 3.) 13. iven ight iocele with leg length j, ight iocele with leg length k, Pove i imila to. j k 8. L 1. iven ectangle JKLM with ide length and, ectangle with ide length and Pove ectangle JKLM i imila to ectangle. K J K P M J M L ection. imilait and anfomation 19

6 15. MODLIN WIH MHMI Detemine whethe the egula-ized top ign and the top ign ticke ae imila. Ue tanfomation to eplain ou eaoning. 19. NLYZIN LIONHIP aph a polgon in a coodinate plane. Ue a imilait tanfomation involving a dilation (whee k i a whole numbe) and a tanlation to gaph a econd polgon. hen decibe a imilait tanfomation that map the econd polgon onto the fit. 1. in. in. 0. HOUH POVOKIN I the compoition of a otation and a dilation commutative? (In othe wod, do ou obtain the ame image egadle of the ode in which ou pefom the tanfomation?) Jutif ou anwe. 1. O NLYI Decibe and coect the eo in compaing the figue. 1. MHMIL ONNION uadilateal JKLM i mapped to quadilateal J K L M uing the dilation (, ) 3, 3. hen quadilateal J K L M i mapped to quadilateal J K L M uing the tanlation (, ) ( + 3, ). he vetice of quadilateal J K L M ae J( 1, 0), K( 1, 18), L(, 18), and M(, 0). ind the coodinate of the vetice of quadilateal JKLM and quadilateal J K L M. e quadilateal JKLM and quadilateal J K L M imila? plain ) ( 1 1 igue i imila to igue. 17. MKIN N UMN membe of the homecoming decoating committee give a pinting compan a banne that i 3 inche b 1 inche to enlage. he committee membe claim the banne he eceive i ditoted. Do ou think the pinting compan ditoted the image he gave it? plain.. PD ONIN Ue the diagam. 8 in. 18 in. a. onnect the midpoint of the ide of to make anothe tiangle. I thi tiangle imila to? Ue tanfomation to uppot ou anwe. 18. HOW DO YOU I? Detemine whethe each pai of figue i imila. plain ou eaoning. a. b. b. epeat pat (a) fo two othe tiangle. What conjectue can ou make? Maintaining Mathematical Poficienc eviewing what ou leaned in peviou gade and leon laif the angle a acute, obtue, ight, o taight. (ection 1.5) 3.. hapte h_geo_pe_00.indd anfomation 1/19/15 10:05 M