Chapter 11 Answers

Chapter 11 Answers (continued)
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Enrichment 11-1
1. Given 2. Two points determine a line segment.
3. Two tangents drawn to a circle from an external point
are congruent. 4. Radii of a circle are congruent.
5. A radius and a tangent drawn to the same point of contact
form a right angle. 6. Definition of a square 7. Sides
of a square are congruent. 8. Addition Property
9. Segment Addition Postulate 10. Substitution Property
11. Addition Property 12. Substitution Property
13. Subtraction Property
Enrichment 11-2
1a. 1 1b. 3 1c. 6 1d. 10 1e. 15
2. 1, 3, 6, 10, 15 3. triangular numbers 4.
2
5. From each point, (N - 1) chords may be drawn. So, a total
of N(N - 1) chords may be drawn for N points. Because each
chord has been drawn twice, divide by 2. 6. N(N - 1)
Enrichment 11-3
1. Given 2. Two points determine a line segment.
3. The measures of exterior angles of a triangle equal the
sum of the measures of the remote interior angles.
4. Radii of a circle are congruent. 5. Definition of
isosceles triangle 6. Base angles of an isosceles triangle
are congruent. 7. Definition of congruent angles
8. Base angles of an isosceles triangle are congruent.
9. Definition of congruent angles 10. The measures of
exterior angles of a triangle equal the sum of the measures
of the remote interior angles. 11. Substitution Property
12. Division Property 13. drawing diameter DE passing
through A so that radius OB AB
Enrichment 11-4
1. 2x + 2x + 8 + x + x - 32 = 360; 6x - 24 = 360;
6x = 384 2. x = 64 3. 128 4. 136 5. 64
6. 32 7. chords ) AB, BD; 16 8. secants EB, EC ; 52
9. tangent FB and chord AB; 64 10. chords
)
BD, AC; 84
11. chords AC, BC; 64 12. tangent FB and secant FD;
36 13. chords AC, BD; 96 14.
)
AF, AE; 100
15. DE, DA; 48 16. tangent FB and chord BC; 68
Enrichment 11-5
1a. the edge of the fountain pool 1b. plaza
N(N 2 1)
1c. fountain pool 2. a circle with center (-3, 4) and a
radius of 3 3. all the interior points of a circle with center
(4, 0) and a radius of "12 4. all points outside a circle
with center (0, 0) and a radius of "18 5. a circle and all
its interior points with center (0, -2) and a radius of 5
6. x 2 + y 2 = 100 7. x 2 + y 2 36 8. The sergeant
can draw a circle with center (0, 0) and a radius of 2. The team
will search in the circle.
Enrichment 11-6
1.–9. Check students’ drawings. 1. P with a radius
of 4 in. 2. two lines parallel to line l, one 2 in. above l
and the other 2 in. below l 3. 4 points 4. two lines
parallel to line l, one 4 in. above l and the other 4 in. below l
5. 2 points 6. two lines parallel to line l, one 6 in. above l
and the other 6 in. below l 7. empty set 8. 6 points
9. empty set
Chapter Project
Activity 1: Doing
Check students’ work.
Activity 2: Exploring
Both figures are made from 9 circles with the same center. In
Figure A, the smallest circle and alternate rings are black. In
Figure B, vertical and horizontal tangents to the smallest circle
are drawn. Then the tangents at 45° angles to the first ones are
drawn. Alternating sections of the 6 outer rings are black, as is
the smallest ring.
Check students’ work.
Activity 3: Constructing
Check students’ work.
✔ Checkpoint Quiz 1
1. 52 in. 2. 44 cm 3. 40 m 4. 6 5. 12
6. 11.5 7. x = 37, y = 100 8. x = 116, y = 88,
z = 79 9. x = 120
✔ Checkpoint Quiz 2
1. x = 140 2. x = 75, y = 105 3. x = 20, y = 70
4. x 2 + (y - 1) 2 = 6.76 5. (x + 3) 2 + (y - 2) 2 = 100
6. 12 7.
51
7
8. 20
Chapter Test, Form A
1. C(0, 0); r = 10 2. C(11, -6); r = 9
3. C(-1, -4); r = "7 4. (x + 3) 2 + (y - 2) 2 = 1
5. (x - 2) 2 + (y - 1) 2 = 16 6. x 2 + (y - 2) 2 = 9
7. C = 31.4; A = 78.5 8. (x + 3) 2 + (y - 4) 2 = 41
9.
y
10. 90
C(1, 2)
r 2
x
Geometry Chapter 11 Answers 35