Chapter • Section 1.1 Chapter GEOMETRY INVESTIGATION Cat Runner Boat 14 squares 12 possible pentominos One solution is shown Many solutions are possible (a) 4 Parallelogram (b) (c) 10 (a) Yes it is possible (b) One possible solution is shown ( Swan Woman 12 To expose the minimum number of faces, stack the cubes as shown: Letters To expose the maximum number of faces is to stack the 18 blocks vertically or horizontally 14 One solution is shown Many solutions are possible 16 82 people, 202 people 18 (a) Copyright © 2012 Pearson Education, Inc Publishing as Prentice Hall (b) • Chapter 20 No, there are four points where three lines meet For at least three of these points, your tracing will take you to the point, away from the point, and then back to the point There is no way to leave any of those points without retracing a line 22 Lines are labeled in the order they can be traced Many tracings are possible One solution is shown 34 36 Four possible solutions are shown 38 Move 1: Move 2: 24 167 m by 668 m 26 200 inches Move 3: 28 Use stacks One stack can contain the 9-inch and a 1-inch box Another stack can contain the 7-inch and the 3-inch box The third stack can contain the 5-inch, 4-inch, and a 1-inch box The remaining stack can contain the rest of the boxes Other arrangements are possible 40 31 rectangles 30 42 2520 ft Finished: 44 (a) One answer is shown Other answers are possible 32 Make the following cut, as shown on the left, and arrange the pieces as shown on the right (b) One answer is shown Other answers are possible Copyright © 2012 Pearson Education, Inc Publishing as Prentice Hall Chapter • 34 (a) 1, 6, 12, 8, (b) 8, 24, 24, 8, 0; 27, 54, 36, 8, (c) (n − 2)3, 6(n − 2)2, 12(n − 2), 8, Selected Extended Problems 46 36 No, it cannot be done Notice the number of black squares and the number of white squares 38 (144)(233) = 33,552 Section 1.2 (a) 3, 5, 7, 9, 11, 13, 15, 17 (b) 20 triangles (c) 2n + toothpicks 6, 10, 14, 4n + 4, 9, 14, 5n − n(3n −1) 10 n(3n − 2) 12 (a) iii (b) ii 14 (a) (b) (d) (e) (c) i (d) iii (c) 16 (a) 19, 22, 37, 3n + (b) 35, 48, 143, n2 − (c) 32, 64, 2048, 2n − −6 −7 −12 −n , , , (d) 13 n + 18 15 paths 40 There are distinct arrangements The greatest area available for the garden, 42 ft2, occurs with the following arrangement Selected Extended Problems 42 The sum of the first n odd-numbered terms of the Fibonacci sequence is equal to the nth even numbered term The sum of the first n evennumbered terms of the Fibonacci sequence is equal to one less than the n+1st odd-numbered term The sum of any 10 Fibonacci numbers is equal to the product of 11 and the 7th number in the sum Ratios of consecutive pairs of Fibonacci numbers, that is, ratios of the (n+1)st divided by the nth Fibonacci number get closer to 1.618, which is an approximation to the golden ratio 43 Number of Bricks Wall Patterns 20 14 paths 22 (a) (b) (c) (d) 19, 31, 50 6, 13, 33 8, 11, 30 13, 23, 36, 59 24 35 triangles 26 19 squares, 2n − 28 52 squares, 5n + 30 44 cubes, 4n + 32 1330 cubes Copyright © 2012 Pearson Education, Inc Publishing as Prentice Hall • Chapter The sequence in the number of possible wall patterns generated is 1, 2, 3, 5, After the first two terms, each new term is created by adding the previous two terms A similar sequence is not generated if the wall is units tall and 1-unit by 3-unit bricks are used The sequence generated is 1, 1, 2, 3, 4, and is not the sum of the previous two terms Copyright © 2012 Pearson Education, Inc Publishing as Prentice Hall ... way to leave any of those points without retracing a line 22 Lines are labeled in the order they can be traced Many tracings are possible One solution is shown 34 36 Four possible solutions are... 24 167 m by 668 m 26 200 inches Move 3: 28 Use stacks One stack can contain the 9-inch and a 1-inch box Another stack can contain the 7-inch and the 3-inch box The third stack can contain the... 4-inch, and a 1-inch box The remaining stack can contain the rest of the boxes Other arrangements are possible 40 31 rectangles 30 42 2520 ft Finished: 44 (a) One answer is shown Other answers are