Lesson 9.3 Relating Congruent and Similar Figures to Geometric Transformations

Transcription

1 Lesson 9. Relating ongruent and Similar Figures to Geometric Transformations State whether the figure and image are congruent or similar.. Rectangle D is rotated 90 clockwise about verte.. parallelogram is reflected in the -ais and then reflected in the -ais.. photocopier dilates a picture b a scale factor of.. trapezoid is dilated with center (0, 0) and scale factor.. heagon is rotated 90 counter clockwise about its center (0, 0) and then dilated b a scale factor of. 6. is mapped onto under a transformation. is the image of under another transformation. 0 a) Describe the transformations that map onto and onto. is mapped onto b using a reflection in the line. is mapped onto b using a rotation of about the point (, ). Marshall avendish International (Singapore) Private Limited. 7 hapter 9 Lesson 9.

2 b) If the order of the transformations is reversed, draw and and on the coordinate plane. c) Do the two triangles have the same coordinates? re the congruent? Eplain. Marshall avendish International (Singapore) Private Limited. Etra Practice ourse 7

3 7. triangle with vertices (, ), (, ) and (6, ) is reflected in the -ais to obtain the image. then is mapped onto shown in the diagram b another transformation a) Draw on the same aes above. b) Describe the transformation that maps onto. c) Describe a single transformation that maps onto. Marshall avendish International (Singapore) Private Limited. 7 hapter 9 Lesson 9.

4 8. triangle PQR with vertices P (, ), Q (, ) and R (, ) is dilated b a scale factor with center P to obtain the image PQR. PQR is then mapped b another transformation onto PQR shown in the diagram. 6 Q Q P P R R a) Draw PQR on the same aes above. b) Describe the transformation that maps PQR on PQR. Marshall avendish International (Singapore) Private Limited. c) Describe a single transformation that maps PQR onto PQR. Etra Practice ourse 7

5 9. is mapped onto under a transformation. is then mapped onto under another transformation. Describe the sequence of transformations from to. a) 0 Marshall avendish International (Singapore) Private Limited. 76 hapter 9 Lesson 9.

6 b) Marshall avendish International (Singapore) Private Limited. Etra Practice ourse 77

7 c) Marshall avendish International (Singapore) Private Limited. 78 hapter 9 Lesson 9.

8 0. Quadrilateral D is dilated with center and scale factor.. It is mapped onto PQRS. The length of is feet and the area of D is square feet. 80 D a) Find mqrs. rea = ft 0 ft b) Find the length of PQ. c) Determine the area of PQRS.. The area of a rectangular postcard is 60 square centimeters. dilated cop has an area of 0 square centimeters. what scale factor is the diagonal of the postcard enlarged? Marshall avendish International (Singapore) Private Limited. Etra Practice ourse 79

9 PX X PX 0 P Q Length of PX 0 0 ft Length of the pole P ft In P, 0 8 ft The distance between the walls is 8 feet. In Q, Q ft The length of pole Q is.6 feet. 9. a) st pair: O DO Eplanation: mo mdo (verticall opposite s) mo mdo (alternate s, D) O DO (equiangular) nd pair: OD OEF Eplanation: mod meof (common ) mod moef (corresponding s, D EF) OD OEF (equiangular) rd pair: O FOE Eplanation: mo mfoe (verticall opposite s) mo mfeo (alternate s, EF) O FEO (equiangular) b) OE is not similar to OF. Eplanation: Onl one pair of angles (OE and OF) are equal. The remaining two pairs are not equal. OE is not similar to OF. Lesson 9.. ongruent. ongruent. Similar. ongruent. Similar 6. a) ; 90 clockwise; 0; 0. b) 0 c) No; the coordinates are different because the order of transformations is reversed. Yes; the size and shape of figures remain the same under translations and reflections. 7. a) b) is mapped onto b a rotation of 90 clockwise about origin O. c) reflection about the line will map onto. 8. a) 6 Q Q Q P P P R R R Etra Practice ourse 8

10 b) P Q R is mapped onto P Q R b a reflection about the line =.. c) dilation of scale factor about the point (, ) will map PQR to P Q R. 9. a) is mapped onto b a translation of units to the right and 6 units up. is mapped onto b a rotation of 90 clockwise about the point (0, ). b) is mapped onto b a reflection about the line. is mapped onto b a dilation of scale factor about the point (, ). c) is mapped onto b a rotation of 90 counter clockwise about the point (, 0). is mapped onto b a reflection about the line. 0. D PQRS a) mqrs md 60 md m md (sum of quadrilateral) PQ b). (scale factor) PQ. PQ.. ft rea of PQRS c) (.) rea of D rea of PQRS (.) rea of PQRS (.) 7 ft The area of PQRS is 7 square feet.. Let the scale factor be k. rea of enlargedcop k rea of original postcard 0 k 60 k k The diagonal of the postcard is dilated b a scale factor of. rain@work. Let the height of the big triangle be p. p m p ( m) p m Eq. p n m p (n m) p n m p m + n Eq. Multipl Eq. b : p ( m) 0p 60 m Eq. Multipl Eq. b : p (m n ) 0p m n 8 Eq. Substitute Eq. into Eq. : 60 m m n 8 60 m 60 m n 8 60 m m n m m m n m m n m n m n. XY Z [common angle] YX Z [corr. s] XY and Z are similar. Y Z Z Z XY Z Y XY XW Z [common angle] WX Z [corr. s] XW and Z are similar. W Z Z Z XW Z XW W So, Y XW XY W. Since XW YZ and WZ XY, Y WZ Y YZ YZ W ZW WV So, Y : YZ ZW : W (shown) umulative Practice for hapters 7 to 9. p 6 8 nswers