Chapter 1 Answers. Reteaching Check students work. 7.

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1 hapter nswers lternative ctivity -4. heck students work.. heck students work. The sum of the measures of the two pieces equals the measure of the whole. 4. same as Eercise 3 5. heck students work. 6. heck students work. 7. The sum of the measures of the two angles in the interior equals the measure of the whole. 8. same as Eercise 7 lternative ctivity -5. heck students work.. heck students work. nswers may vary. ample: erpendicular lines form right (90 ) angles. 4. nswers may vary. ample: erpendicular lines are lines that meet at 90 angles. 5. heck students work. 6. heck students work. 7. heck students work. 8. nswers may vary. ample: n angle bisector is a ray that breaks an angle into two congruent angles. 9. heck students work. lternative ctivity -7. heck students work.. heck students work. nswers may vary. ample: djacent angles are supplementary. Non-adjacent angles are congruent. 4. ngles change measures but statements given for eercise 3 still hold. eteaching eteaching heck students work. 7. y O T 8. nswers may vary. ample: T nswers may vary. ample: and T eteaching -3 nswers may vary. amples:. and EF. and DH and E 4. plane D and plane EFH 5. plane DH and plane FD 6. plane DH plane G and plane D 7. EG and F rentice-hall Inc Geometry hapter Tools of Geometry 47

2 hapter nswers (continued) eteaching -4 a. Each angle is 08. b. obtuse a. Each angle is 7. b. acute 3a. Each angle is 08. 3b. obtuse right acute 6. 0 obtuse acute right obtuse eteaching -8. y eteaching -5 nswers may vary. amples:. D D. D and D and EF D DE 4. D and E D and F 5. D and DFE D and D 6. D; D EF 7. D D and FG 0. E and ED. D and Z eteaching -6 nswers may vary. amples: Z 4. Z > ractice -: Eample Eercises. Decrease by 3 then 4 then 5 etc.. 35 No; eventually this pattern will produce negative absences which is meaningless based on the pattern shown in this table: points segments onjecture: the sum is always 0. ee table. n sum from n to n yes 8. no 9. The argument works only for p 000. ut p can be any integer and for p 000 the argument fails. 0. Maybe L is the largest number. ut L is larger so maybe L is the largest number. ut L is larger than L ; and so on. o it appears that there is no largest number. eteaching nswers may vary. ample: m 0 m 6 80 by the ngle ddition ostulate. m 6 m 7 m 8 80 by the ngle ddition ostulate. m 0 m 6 m 6 m 7 m 8 by the Transitive roperty of Equality. ubtract m 6 from both sides and you get m 0 m 7 m 8. ince 0 is a right angle m 7 m It is given that m 7 m 8. y substitution m Divide both sides by and m nswers may vary. ample: ecause 9 and 0 form a straight angle m 9 m 0 80 by ngle ddition ostulate. y definition of supplementary angles 9 and 0 are supplementary. 48 Z ractice -: Mied Eercises nswers may vary. ample: or or or 8 0. or. D or G. or any heagon 4. circle with 8 equally spaced diameters 5. a angle 6. handshakes 7. n(n ) nswers may vary. ample: The farther out you go the closer the ratio gets to a number that is approimately ractice -: Eample Eercises. yes. no yes 4. any two of the following: FGD FGE FDE or GDE. (The three letters can be written in any order.) 5. yes 6. yes 7. no 8. plane T 9. T 0. T. T. the empty set T collinear 7. collinear 8. noncollinear Tools of Geometry Geometry hapter rentice-hall Inc.

3 hapter nswers (continued) 9. coplanar 0. coplanar. noncoplanar. coplanar coplanar 4. coplanar 5. coplanar 6. coplanar 7. noncoplanar 8. yes 9. no ractice -: Mied Eercises.. any two of the following: D D E E ED DE E D oints E and D are collinear. 4. yes 5. yes 6. no 7. no 8. yes 9. no 0. yes. yes. yes no 4. yes 5. yes 6. G 7. LM 8. N 9. the empty set 0. K. M. plane D plane yes 6. no 7. yes 8. the empty set 9. no 30. yes yes ractice -3: Eample Eercises. parallel. parallel intersecting 4. parallel 5. skew 6. intersecting 7. intersecting 8. skew 9. false 0. true. false. true 5. nswers may vary. amples: ractice -3: Mied Eercises. true. false true 4. false 5. false 6. false 7. JK HG 8. EH 9. any three of the following pairs: EF and JH; EF and GK ; HG and JE ; HG and FK ; JK and EH ; JK and FG; EJ and FG ; EH and FK. 0. planes and. planes and ; planes and. planes and planes and 4. EG EF and ED or EG and ED 7. FE FD 8. GF GD 9. yes 0. nswers may vary. ample: T U. nswers may vary. ample: W J rentice-hall Inc W K T ractice -4: Eample Eercises z ; 39; ; DE 4; EF 4 9. y 0; GH 9; HI 3 ractice -4: Mied Eercises or 6 7. or 8. any three of the following: O MO OM D DE EF DF F F D E E 3; 3; ; 03; 03 ractice -5: Eample Eercises. 5. nswers may vary. amples:. Other vehicles such as trucks fit this description.. Other objects such as spheres are round. not specific enough; many numbers in a set could fit this description. 4. need to distinguish cricket from baseball which also fits this definition. 5. leasing smooth and rigid are all too Geometry hapter Tools of Geometry 49

4 hapter nswers (continued) vague. 6. yes 7. no 8. yes 9. 4; m D y 7; m ractice -5: Mied Eercises. a and b. 6. nswers may vary. amples:. No; not all apples are green. lso there are other juicy green fruits such as pears. No; beautiful and fragrant are too vague. 4. No; triangles are made of segments (joined at their endpoints) not lines. 5. No; other instruments such as violins fit this description. 6. No; while almost acceptable more information is needed to distinguish it from other practices. 7. true 8. false 9. false 0. true. true. true false 4. ; m D O m ractice -6: Eample Eercises. c b 9. M. a N 0. r q. p rentice-hall Inc. 6. m 50 Tools of Geometry Geometry hapter

5 hapter nswers (continued) 6. MN O 7. K O L MN D ractice -6: Mied Eercises. 8. m m. 9. m m m m 0. m m. 4.. rentice-hall Inc. 5. Z m W m Z Z Geometry hapter Tools of Geometry 5

6 hapter nswers (continued) 4. true 5. false 6. false 7. true 8. true 9. false 0. true y ractice -7: Eample Eercises y y and 3; and 4 9. any two of the following pairs: ; 3; 3 4; angles and 3; angles and supplementary supplementary 5. Let m m 3. Then m 80 and m o m m (5 3) ractice -7: Mied Eercises false 8. true 9. true 0. true. false. false false 4. true 5. true 6. false 7. false 8. m MO 55; m M 5; m MN m OD m OE 90; m O m OD 45; m O m DOE m W m WD; m W m W 80; m WD m DW 80; m W m WD ractice -8: Eample Eercises a b a. They are equal. 4b. 5. ( 7) 6. (0 0) 7. ( 3) 8. ( 4 9) 9. ( ) ( ) (.5 3) heckpoint : For use after G 4. ny three points are coplanar. 5. intersecting 6. parallel 7. parallel 8. skew 9. heckpoint : For use after nswers may vary. amples:. two angles whose measures add to 80. angle with measure less than 90 a point on a line together with all the points on one side of that point. 4. an area specifically designated for outdoor recreation usually for children. 5. two intersecting lines that form right angles 6a. b. ractice -8: Mied Eercises. 5. y 7. / D E hapter ssessment Form rentice-hall Inc (5 5) ( ) 4. ( 0 5) 5. ( 6) 6. ( 0.3 4) 7. ( ) 8. (5 ) 9. (4 0) 0. ( 3 4). es; D D a. 4b. 4c any of the following: O ; O D; E O F 6. nswers may vary. ample: O and F 5 Tools of Geometry Geometry hapter

7 hapter nswers (continued) 7. nswers may vary. ample: G E F and 8a. O 8b. EF 8c. O 8d. G 9. nswers may vary. amples: 9. No; a ray is that part of a line consisting of one endpoint and all the points of the line that are on one side of the endpoint. 0. No; a basket is a receptacle usually made of interwoven material.. No; parallel lines are coplanar lines that do not intersect.. yes No; a spoon is an eating or cooking utensil consisting of a small shallow bowl with a handle D blocks. ( 3 ) (4 ) a. M 8b. M 8c. F 8d. O 9.. nswers may vary. ample: 9. No; vertical angles are the non-adjacent angles formed when two lines intersect 0. No; a sweater is a knitted or crocheted jacket or pullover.. No; congruent angles are angles with the same measure.. No; the midpoint of a line segment is the point on the segment that divides the segment into two congruent segments. yes D blocks. ( 4 ) (9 8) rentice-hall Inc. hapter ssessment Form nswers may vary. ample: 4a. 5 4b. 9 4c nswers may vary. ample: 5. M E and D 6. M and O 7. F O and D lternative ssessment TK : coring Guide nswers may vary. amples: a. Eterior rays form a right angle for each figure. The total number of rays doubles with each successive figure. Two parallel segments connect the innermost rays. b. Other answers are possible. For eample instead of considering the total number of rays ( 4 8 6) consider the rays in the interior of the right angle: In that case you can argue that comes net giving a total of 4 rays not 6 in figure 4. c. ame as in b ecept with 3 rays. Geometry hapter Tools of Geometry 53

8 hapter nswers (continued) TK : coring Guide (cont d) 3 tudent gives correct eplanation clear descriptions and an accurate drawing. tudent gives eplanations descriptions and a drawing that are generally clear but may contain several errors. tudent makes significant errors in eplanations and descriptions. 0 tudent makes little or no attempt. TK : coring Guide a. nswers may vary. ample: b. No because any three points are coplanar. c. nswers may vary. ample: and 3 tudent gives an accurate diagram correct answers and a valid eplanation. tudent draws a diagram that contains some errors but gives answers to parts b and c that are correct. tudent draws a diagram that contains significant errors and gives answers to parts b and c that are incorrect. 0 tudent makes little or no attempt. TK 3: coring Guide nswers may vary. ample: E D (90 m ) 3 tudent constructs figures correctly. tudent constructs figures but construction may contain some minor errors. tudent misses some key ideas resulting in significant errors in the constructions. 0 tudent makes little or no attempt. G TK 4: coring Guide nswers may vary. ample: V T a. ; the midpoint is ( ). b. T and V; V and V; V and T; T and T; T and V; T and V c. Of the si pairs listed in part b the first four are linear pairs. d. T and V; T and V e. T is a right angle because the lines are perpendicular. o m 90. Therefore if bisects T m tudent draws a diagram and gives responses that indicate thorough understanding of the definitions involved. tudent shows logic in part e that is eemplary. tudent draws a diagram and gives responses that while basically accurate contain some minor flaws inaccuracies or omissions. tudent gives logical argument in part e. tudent draws a diagram or gives responses that contain significant inaccuracies or omissions. tudent displays logical flaws in argument in part e. 0 tudent makes little or no attempt. umulative eview.. 4. D 5. D D D.. 4. nswers may vary. ample: and The first is the natural numbers. In the second the numbers and 3 repeat. 5. nswers may vary. ample: T and VW 6. and V 7. W U V 8. always 9. never 0. not acceptable; too general; answers may vary. ample: chair is a piece of furniture designed to be sat upon by one person. rentice-hall Inc. 54 Tools of Geometry Geometry hapter

9 hapter nswers (continued). nswers may vary. ample: E F. nswers may vary. ample: 45 ( 4 ) 4. (0 3) 5. 9 tandardized Test ractice D D D D and and are collinear. o is the midpoint of. nswers may vary. ample: These angles are supplementary: and and 3 3 and 4 and 4. These angles are congruent vertical angles: and 3 and rentice-hall Inc. Geometry hapter Tools of Geometry 55