2.1 Start Thinking! For use before Lesson Warm Up. For use before Lesson not congruent 2. not congruent 3.

Transcription

1 0. a.. a. d = b. π 8 in. π c. in. c = b. 7 ft c. 8 ft d. Practice. = 8 + x.. π = x 8 = + 0.8x. =.6 + x a. = V w h 8. b. 7 ft T hp = 7. x =. 80 S r h = π r 0. a. ( F ) 9. P = a = b. 00 c a. m = b.. πr c. greater than; The numerator will be larger.. Enrichment and Extension. The height is about. feet using both methods.. Sample answer: Method ; ecause ou can do all of the calculations in one step.. Puzzle Time RIVER Technolog onnection. x =. x =. x = or.. Start Thinking! For use before Lesson.. es; onsider two equilateral triangles, one with -inch sides and another with -inch sides. oth have three 60 angles, but the are not congruent because the corresponding sides are not congruent.. no; onsider two triangles made from toothpicks that have side lengths of centimeters, 6 centimeters, and 7 centimeters. No matter how ou arrange each set of toothpicks, the will alwas form two congruent triangles.. Warm Up For use before Lesson.. not congruent. not congruent. not congruent. congruent not congruent congruent. Practice. congruent. not congruent. orresponding angles: and D, and E, and F orresponding sides: side and side DE, side and side EF, side and side FD. orresponding angles: G and K, H and L, I and M, J and N orresponding sides: side GH and side KL, side HI and side LM, side IJ and side MN, side JG and side NK not congruent; orresponding side lengths are not congruent. congruent; orresponding side lengths and corresponding angles are congruent. 7. The corresponding sides are not congruent, so the two figures are not congruent. hapter. Start Thinking! For use before ctivit. heck students sketches.. Warm Up For use before ctivit.. in., in., in.. in., in., in no; ongruent polgons have congruent angles. Thus, both polgons would have a right angle.. Practice. orresponding angles: and J, and K, and L, D and M orresponding sides: side and side JK, side and side KL, side D and side LM, side D and side MJ. in., in., in in., in., in opright ig Ideas Learning, LL

2 . orresponding angles: P and V, Qand W, R and X, S and Y, T and Z orresponding sides: side PQ and side VW, side QR and side WX, side RS and side XY, side ST and side YZ, side TP and side ZV. not congruent; orresponding side lengths are not congruent.. congruent; orresponding side lengths and corresponding angles are congruent. a. 0 in. b. L c. in. a. true; The have the same mark. b. false; side MN is congruent to side ED. c. false; corresponds to P. d. true; corresponds to P and corresponds to O. So, side is congruent to side PO. e. true; m = 90. m = m = m O = 0. m D = m N = 0. So, the sum is = 0. f. false; and m = 0. So, m = 0.. Enrichment and Extension. The lengths of the sides in Triangle are times larger than the lengths of the sides in Triangle.. cm. 60 cm. The perimeter of Triangle is times larger than the perimeter of Triangle. In Exercise, it was observed that each length in Triangle was times larger than that of Triangle. 6cm 0 cm 7. The area of Triangle is times larger than the area of Triangle. 8. The side lengths of Triangle are times larger than the side lengths of Triangle. ecause area is a two dimensional measurement, ou can predict 9. that the area of Triangle will be or ( ) or times larger than the area of Triangle. 6 cm 0. no; If all the sides did not increase b the same factor, ou could not predict the total change in perimeter or area. opright ig Ideas Learning, LL. Puzzle Time KED EINGS. Start Thinking! For use before ctivit. Sample answer: architect, engineer, interior designer. Warm Up For use before ctivit. N(, ) S(, 0) R(, 0) x P(0, ) T(, ). Start Thinking! For use before Lesson. Sample answer: athroom tile because the tile fits together without space.. Warm Up For use before Lesson.. no. es. no. es. Practice. es. no. P (, ), Q (, ), R (, ). units left and units down 7. units right and units up. Practice. no. es. T (, ), U (, ), V (, ), W (, ). units left and units down 7 units up Q(, ) x x a. unit right and 7 units down b. unit left and 7 units up

3 7. a. es b. no c. es. Enrichment and Extension. : right and down ; : right and down ; : right and down ; D: right and down ; E: down ; F: left and down ; G: left and down. : left and down ; : left and up ; : left and down ; D: left and up ; E: left and up ; F: left and up ; G: left and up. : down ; : left and down ; : down ; D: left and down ; E: left 6 and down 6; F: left. and down ; G: left 6 and up ; or : down ; : left and down ; : down ; D: left and down ; E: left 6 and down ; F: left. and down ; G: left 6 : right 7 and up ; : right 6 and up ; : right and up 8; D: right and up ; E: up ; F: right and up 7; G: up ; or : right 6 and up ; : right 6 and up ; : right and up 8; D: right and up ; E: right and up ; F: left and up ; G: up nswer should include, but is not limited to: The puzzle should have seven tans that can form the shape without overlapping the tans. Some puzzles will have more than one solution.. Puzzle Time DRKNESS. Start Thinking! For use before Lesson. Sample answer: radar and civic; Palindromes like mom are reflections. Palindromes like pop are not reflections.. Warm Up For use before Lesson.. no. es. no. es. Practice. es. no.. O E ( 0, ), (, ), (, ) E F G H I E F F (, ), (, ), (, ) H I J G x G O x J H I J. Start Thinking! For use before ctivit. Sample answer: n airplane glides out of its gate then down the runwa. It travels from one point to the next. When it reaches its destination it lands on the runwa and taxis to the gate.. Warm Up For use before ctivit... x x Y Y x X X Z Z ( 0, ), (, ), (, ) X Y Z U W W U x V V 6 (, ), (, ), (, 0 ) U V W opright ig Ideas Learning, LL

4 7. WOW 8. -axis 9. x-axis 0.. Quadrant III. Practice. no. es. K M L O x L M K P Q R x N N (, ), (, ), (, ), (, ) K L M N (, ), (, ), (, ), (, ) G H I J 7. bob 8. x-axis 9. -axis 0. I I H J H x J G G x K J L. a. (, ), (, ), (, ) b. Each coordinate in the resulting triangle is the opposite of its corresponding coordinate in.. Q P O R x O R P Q (, ), (, ), (, ), (, ) O P Q R. Enrichment and Extension Figures and H cannot be created using the Master. Sample answer: : : D D D: E: E E x (,, ) (,, ) (,, ) (,0) D E F: G: opright ig Ideas Learning, LL 7

5 I: J: (, ), (, 0 ), (, ), D (, ) ( 9, ), ( 8, 0 ), ( 6, 0 ), D (, ) 7. no 8. es. Puzzle Time OT OF PINT. Start Thinking! For use before ctivit. Yes, the 0-ard line. Sample answer: football field is a reflection of itself over the 0-ard line.. Warm Up For use before ctivit.. D (, ) E (,, ) F (,, ) G (, ). H (, ), I (, ), J (, ), K (, ). Start Thinking! For use before Lesson. Sample answer: translation: how the plaers move down the court; reflection: the basketball court; rotation: a plaer using his pivot foot when he has the ball.. Warm Up For use before Lesson.. translation. reflection. rotation. Practice. es; 80 clockwise. no. (,, ) (,, ) (, ). (,, ) (,, ) (, ) (, ), (, ), (, ) (, ), ( 0, 0 ), (, ) 7. es 8. no. Practice. no. es; 90 counterclockwise. (, ), (, ), (, ), D (, ). (, ), (, ), (, ), D (, ). Enrichment and Extension. Sample answer: Rotate 90 degrees clockwise about the origin. Reflect in the x-axis. Translate units left and units up. Rotate 80 degrees about the origin.. Translate units down. Rotate 80 degrees about the origin. Reflect in the -axis. Rotate 90 degrees counterclockwise about the origin. Translate unit right.. Sample answer: Rotate 90 degrees clockwise about the origin. Reflect in the -axis. Reflect in the x-axis. Rotate 90 degrees counterclockwise about the origin. Translate units down.. Sample answer: Translate units up. Reflect in the x-axis. Rotate 80 degrees about the origin. Translate units left. Rotate 90 degrees counterclockwise about the origin. Reflect in the -axis.. Puzzle Time TRFFI JM. Start Thinking! For use before ctivit. Sample answer: Drawing a sketch of our garden that is proportional to the actual garden will help ou bu the correct number of seeds to plant.. Warm Up For use before ctivit.. es. no. no. no es es. Start Thinking! For use before Lesson. Sample answer: Two figures are similar if their sides are proportional.. Warm Up For use before Lesson.. es; The sides are proportional.. no; The sides are not proportional.. es; The sides are proportional.. es; The sides are proportional. 8 opright ig Ideas Learning, LL

6 . Practice. orresponding angles: and D, and E, and F orresponding sides: side and side DE, side and side EF, side and side DF. es; orresponding angles are congruent and the ratio of the lengths of corresponding sides is.. no. a. no b. es in. b in.; in. b. in.. Practice. and ; orresponding sides and corresponding angles are congruent.. es O x O x. orresponding angles: P and T, Q and U, R and V orresponding sides: side PQ and side TU, side QR and side UV, side PR and side TV a. no b. es c. no d. es 9. no; The angles will be corresponding, so the triangles will be similar. 0. a. Sample answer:,, and b. Sample answer:, 8, and c. es. Enrichment and Extension. Sample answer: house or other object might be blocking the path of our character. So, ou could use a laser to shrink it so that ou can get to a prize or safet. You might use a laser to enlarge a suppl of food or other supplies. O x. a. (, ), (, ), (, ),,,,, b. ( ) ( ) 0,,,,,,, 6, E (, 6 ), F,,, G. a. ( ) D ( ),,, 0,, 0,,, D E,,, 0, (, 0) F G b. ( ) ( ). a. ( ) ( ) ( ) D E ( ) F,, 7, 9, 7, 9, 9, 6,, 9,,, G 8, 9, H, 6, I, 9, J, 9 ( ) ( ) ( ),0,,,,, D,,,,,, E F G,, H,, I(, ), J, b. ( ) ( ) ( ) The area of the enlarged triangle is 9 times larger, which is squared. ecause area is in square units, the factors are squared. So, if the base and height are times larger, ou square that factor to find how much bigger the area is.. Puzzle Time THE IYLE THT KEPT FLLING OVER EUSE IT WS TWO TIRED.6 Start Thinking! For use before ctivit.6 Sample answer: You need to find the area of our room b measuring the length and width..6 Warm Up For use before ctivit.6. P = in.; = 6 in.. P = 60 cm; = cm. P = cm; = 6 cm. P = 8 in.; = 0 in. opright ig Ideas Learning, LL 9

7 .6 Start Thinking! For use before Lesson.6 When our neighbor doubles the side lengths of the deck, the perimeter of the deck will double in size..6 Warm Up For use before Lesson.6. The perimeter will quadruple.. The area will double.. The perimeter will triple.. The perimeter will double..6 Practice. Perimeter: : 9; rea: : 8. Perimeter: : 7; rea: 9 : 9. Multiplies it b.. a. : b. 6 : c. ft x = 0 a. b. in. c. : 7 d..6 : 9.6 Practice. Perimeter: : ; rea: : 69. Multiplies it b.. x = 0.. a. 9 : b. 8 : 96 c. 70 ft a..6 times greater b. a. : b. : c. π.6 Enrichment and Extension. $ in. in. in. in.. $8.87. in. 98 in.. ft c. ft 8 in. 8 in. 7 in. 7 in. 69 in. 7% 7. Sample answer: utting straight rectangles is eas to do, and then the do not have to find a use for the left over material that is oddl shaped. 8. Sample answer: She could make more frames that are smaller. She could use the material as a rag for household cleaning. She could use it as a drop cloth to protect small surfaces near where she is painting or doing other crafts..6 Puzzle Time TO THE WSPITL.7 Start Thinking! For use before ctivit.7 Sample answer: photos.7 Warm Up For use before ctivit Start Thinking! For use before Lesson.7 Sample answer: photographer ma need to enlarge or reduce a photo to fit a specific spot in a magazine..7 Warm Up For use before Lesson O 6 0 x The triangles are similar..7 Practice (0, 0) (, ) (, ) 6 7 x The triangles are similar. (6, ) O x The triangles are similar. (, 9) (, ) 0 8 O (, ) ( 9, 6) 0 (, ) The triangles are similar. 6 x (, ) (6, 6) 0 opright ig Ideas Learning, LL

8 . es. no reduction enlargement 7. reduction; 9. k = 8. enlargement; k = 0. P ( 6, ), Q ( 0, ), R (, 9).7 Practice.. (, ) (, ) (, ) (, ) (, ) x The triangles are similar. The triangles are similar. (8, ). no. es opright ig Ideas Learning, LL D (, 0) 9 E 6 D(, ) (0, ) (, ) E(, ) 9 G x F(, ) 6 G (, 0) 9 (0, ) (0, ) (, ) (, ) (, 9) ( 60, 90) ( 0, 0) F (, ) (, 6) 9 x O ( 0, 0) 0 60 ( 0, 60) 60 0x (0, 0) (0, 0) enlargement reduction 7. reduction; k = 8. enlargement; k = ; 60 ; perimeter of image is times larger 0. 6 ( 0, 0) 0 (, ) 0 (, ) 0 0 x 0 (, ) (, ) ( 0, ) (, 0) E Enrichment and Extension. no; Dilating an object changes its size but not its orientation. Flipping the surfboard would require a reflection.. inches wide,. inches long. inches wide, 7 inches long. a. scale factor = b. 00% increase a. scale factor = b. 0% decrease The scale factor used to increase the width is different from the scale factor used to increase the length..7 Puzzle Time DO-TOPUS 0 0 D (, ) E ( 7, ) G (, ) 0 D(0, 0) 0 0 x F (, 6) G(, 0) F(, 0) Technolog onnection. The reflected triangle also moves so that it is still a mirror image of the original triangle.. The dilated triangle is a different size than the original triangle, but it is similar to the original triangle.

9 . The closer the center of rotation is to DEF, closer the rotation. hapter. Start Thinking! For use before ctivit. the Sample answers: vertical window blinds, lines formed b floor tiles, top and bottom of walls, the edges of rectangular objects. Warm Up For use before ctivit.. x = 8. x =.. x = 0. x = x =. Start Thinking! For use before Lesson. x = es; You know that three of the angles are congruent to the given angle. The other four angles are supplementar to the given angle (or congruent angles) because the form straight angles.. Warm Up For use before Lesson.. k and. m ; 7. Practice. m = ; m = 6. m = 06 ; m = 7. m = m = 9 (supplementar) m = (vertical) m = m 6 = 9 (corresponding) m = m 7 = (corresponding). m 6 = m 7 = 6 (supplementar) m = 7 (vertical) m = m = 7 (corresponding) m = m = 6 (corresponding) 8 60 ; and are corresponding angles. 7 ; 6 and are vertical angles ; Sample answer: 8 and are corresponding angles, and and are supplementar angles ; and are supplementar angles. 9. is congruent to. is congruent to 8. So, is congruent to is supplementar to. is congruent to. So, 6 is supplementar to.. Practice. m 6 = m 7 = (supplementar) m = 8 (vertical) m = m = 8 (corresponding) m = m = (corresponding). m = 90 (vertical) m = m = 90 (supplementar) m 6 = m = 90 (corresponding) m = m 7 = 90 (corresponding). 0 ; and 8 are corresponding angles.. 7 ; Sample answer: and are corresponding angles, and and are supplementar angles. 09 ; 7 and are supplementar angles. ; Sample answer: and are corresponding angles, and and 6 are supplementar angles. 7. alwas; The are vertical angles. 8. sometimes; The are supplementar if the are right angles. 9. never; The are supplementar. 0. never; The are adjacent angles.. alwas; ngles and 6 are congruent because the are corresponding angles. ngles 6 and 8 are congruent because the are vertical angles. So, angles and 8 are congruent.. no; n two adjacent angles will be supplementar and two acute angles cannot be supplementar.. Enrichment and Extension.,89,89. es; One angle is because of vertical angles, and the other two are 89 because of alternate interior angles. opright ig Ideas Learning, LL