1. Chapter 2 Geometry
Homework Answers

2. Sec 2.1
1) “All rocks sink.” Stony needs to find one rock that will not sink.
15, 21, 28, 36, 45
Answers will vary.
2) If two angles are formed by drawing a ray from a line, then their measures add up to 180°.
Conjecture is false; 14² =196 but 41² =1681
3) 10000, ,….Each term is 10 times the previous term.
23-25) See diagrams.
Collinear
4) 5/6, 1,….(Written with the common denominator of 6, the pattern becomes 1/6, 2/6, 3/6, 4/6, 5/6, 6/6,…)
Isosceles
Protractor
5) -17, -21
Radius
6) 28, 36
Diagonal
7) 21, 34
Dodecagon
8) 49, 64
Parallel
9) -10, -24
Regular
10) 64, 128
90°
11-16) See diagrams.
Perpendicular
1, 4, 7, 10, 13
39-42) See diagrams.

3. Sec 2.2 Inductive; deductive 900, 1080
m ‹ B= 65°; deductive or inductive
75, 91
Inductive
4/5, 12
DG= 258 cm; deductive
15-18) See diagrams.
180° ; 180° ; sum of the five angles is 180° ; inductive L M
LNDA is a parallelogram; deductive A
3; 10; 7 B
Just over 45°; if m > 90°, then ½ m > 45° E
If 11,111 is multiplied by itself, then the product will be 123,454,321. But when 1,111,111,111 is multiplied by itself, the digits can’t go up to 10. So 1,111,111,111x 1,111,111,111=1,234,567,900,987,654,321. C G D H
The pattern cannot be generalized because once the river is straight, it cannot get any shorter. I

4. Sec 2.3
6n-3; 117
-3n+4; -56
8n-12; 148
16, 24, 32, 40, 48; 8n; 1600
1, 9, 13, 17, 21; 4n-3; 797
13, 17, 21, 25; 4n+1; 801
11, 14, 17, 20; 3n+2; 602
1, 2, 3, 4; n-2; 33
Slope: (9-6)/ (4-2)= 3/2; y-intercept: (0,3); y=1.5x+3
10-11) See diagrams.
17) 48°; 17°; 62°; m ‹ CPB

5. Sec 2.4
4, 6, 8, 10; 2n; 70
If n(n-1)/2=66, then n(n-1)=132. What two consecutive numbers multiply to equal 132? 12 times 11. Thus, there were 12 people at the party.
n+1, 36
n-3, because you can draw a diagonal from one vertex to all the other vertices except three of them, the two adjacent vertices and the vertex itself; 32
True
False; an isosceles right triangle has two sides congruent.
See diagram. n(n-3)/2, 560
See diagram. n(n-1)/2, 595
False; see diagram.
False; they are parallel.
See proof.
Use n(n-1)/2 to get 780 direct lines. Use a central hub with a line to each house to get lines.
False; a rectangle is a parallelogram with all of its angles congruent.
False; a diagonal is a segment in a polygon connecting any two nonconsecutive vertices.
Use points for the 10 teams and segments connecting them to represent four games played between them. So, use 4x [n(n-10/2] to get 180 games played.

6. Sec 2.5 a = 60, b = 120, c = 120 See description.
22.5
a = 77, b = 52, c = 77, d = 51
22, 26, 30; 4n + 6; 806
a = 60, b = c = 120, d = f = 115, e = 65, g = i = 125, h = 55
handshake problem: n(n-1)/2; 80(79)/2 = 3160 pieces of string
a = 90, b = 163, c = 17, d = 110, e = 70
3160 intersections
The measures of the linear pair of angles add up to 170, not 180.
n(n-2)/2 yields 760 handshakes.
21; 252
The best angles at which he should cut measure 45.
n(n-3)/2 = 560; there are 35 vertices.
Greatest: 120. Smallest: 60.
The converse is not true.
each must be a right angle
Let the measures of the congruent angles be x. They are supplementary, so x + x = 180, 2x = 180, x = 90. Thus each angle is a right angle.
Answers in degrees unless otherwise labeled.

7. Sec 2.6 63 90 no 57
yes
113
a = d = 64, b = c = 116, e = g = i = j = k = 108, f = h = s =72, m = 105, n = 79, p = 90, q = 116, t = 119
= 170 ≠ 180. Thus, the lines marked as parallel cannot really be parallel.
Alternate interior angles measure 55, but ≠ 180.
The incoming and outgoing angles measure 45. See diagram.
18 cm
Answers in degrees unless otherwise labeled. 39
3486

8. Using Your Algebra Skills 2: Slope-2
-12/13
97/46 ≈ 2.1
y = 23
x = 4
Any point of the form (3p, -4p).
≈ 66.7 mi/hr
At 6 m/sec Skater 1 is 4 m/sec faster than Skater 2 at 2 m/sec.

9. Ch 2 Review
poor inductive reasoning, but Diana was probably just being funny
n², 30² = 900
n(n +1)/2, (100)(101)/2 = 5050
91, 105
n(n – 1)/2 = 741. Therefore, n = 39.
V, 16
n(n – 1)/2, 28(27)/2 = 378
19, -30
n(n – 1)/2 = Therefore, n = 77.
S, 36
n – 2, 54 – 2 = 52
2, 5, 10, 17, 26, 37
n – 2 = 54. Therefore, n = 56.
1, 2, 4, 8, 16, 32
a = 38, b = 38, c = 142, d = 38, e = 50, f = 65, g = 106, h = 74
See diagram.
-3n + 5; -55
Answers for #26 in degrees
n²; 400
n(n - 1)/2; 190
n(n + 1)/2; 210
30² = 900
(30)(31) = 930