Download CCG_SA_Ch6

6-4.
a: Alternate interior angles.
b: Vertical angles.
c: ∠u & ∠z,
∠s & ∠x,
∠v & ∠w,
and ∠t & ∠y
a: They are similar by SAS ~.
6-5.
b: Yes, because they are similar and the corresponding sides have a ratio of 1.
6-6.
3x +1° + 52° = 180° , x = 1273 ! 42.33°
6-7.
a: 8 cm
b: ≈
14.97 ft
c: ≈
15.2 in.
6-8.
1a and 1b: statements ii and iv, 2: The cupcakes are burned, 3: The fans will not buy the
cupcakes because they are burned, 4: The team will not have enough money for uniforms.
6-9.
a: 34 or 75%
c: 1 or 100%
6-1
0.
b: 320 or 15%
c: (b) is an intersection, and (c) is a union.
A
a: Not similar because there are not three pairs of corresponding angles that arecongruent.
b: Similar (AA ~)
6-2
Lesson
6.1.2
3.
6-2
a: y = 52 x ! 8
b: y = 32 x +1
6-14.
4. a = 97º, b = 15º, c = 68º, d = 68º
2 = 10
DE , DE ≈
6-2 a: b:
6-15.
≈ 142
3.75,
tangent
5.
15.71
! 9.9 ,
6-2 b:
a: 72
Yes because
of AAS ≅ or ASA ≅; ΔDEF ≅ ΔLJK. b: One possible answer, a
c: ≈ 9.54, Law
of Cosines 6-16. a: 25 units b: 56 sq. units and 350 sq. units
Pythagorea
6.
reflection across line segment JK and then a translation of ΔDEF to line up point J and
n Theorem
6-17. a: A′(–2,
–7), B′(–5, –8), C′(–3, –1)
point E, followed by a rotation. c: KL ≈ 4.3 units
or 45°-45°
-90° ratios
6-2 b: A″(2, 7), B″(5, 8), C″(3, 1)
c = 10 by substitution.
c:7.Reflection across the y-axis. 6-18. a: (0.8)(0.8)= 0.64 = 64% b:
6-2
(0.8)(0.2)
= 0.16 = 16%
8.
a: P(A or B) = P(A) + P(B) – P(A and B) = 64212 + 112212 ! 0 = 176212 " 83.0% ; the
probability of A and B (the overlap) was 0. b: P(A or B) = P(A) + P(B) – P(A and B) !
75%= 114212 + 56212 ! x " x # 5.1%
6-19. A11
16
19
8
118
13
6
11
2
11
2
14
16
6-4.
a: Alternate interior angles.
b: Vertical angles.
c: ∠u & ∠z,
6-5.
∠s & ∠x,
∠v & ∠w,
and ∠t & ∠y
a: They are similar by SAS ~.
b: Yes, because they are similar and the corresponding sides have a ratio of 1.
6-6.
3x +1° + 52° = 180° , x = 1273 ! 42.33°
6-7.
a: 8 cm
b: ≈ 14.97 ft
c: ≈ 15.2 in.
6-8.
1a and 1b: statements ii and iv, 2: The cupcakes are burned, 3: The fans will not buy the
cupcakes because they are burned, 4: The team will not have enough money for uniforms.
6-9.
6-1
0.
6-2
3.
6-2
4.
6-2
5.
6-2
6.
6-2
7.
6-2
8.
19
118
16
a: 34 or 75%
c: 1 or 100%
b: 320 or 15%
c: (b) is an intersection, and (c) is a union.
A
a: Not similar because there are not three pairs of corresponding angles that arecongruent.
b: Similar (AA ~)
a: y = 52 x ! 8
b: y = 32 x +1
b: 1422 = 10 DE , DE ≈
15.71
a: Yes because of AAS ≅ or ASA ≅; ΔDEF ≅ ΔLJK. b: One possible answer, a
reflection across line segment JK and then a translation of ΔDEF to line up point J and
point E, followed by a rotation. c: KL ≈ 4.3 units
c = 10 by substitution.
a: P(A or B) = P(A) + P(B) – P(A and B) = 64212 + 112212 ! 0 = 176212 " 83.0% ; the
probability of A and B (the overlap) was 0. b: P(A or B) = P(A) + P(B) – P(A and B) !
75%= 114212 + 56212 ! x " x # 5.1%
11
8
16
13
6
11
2
11
2
14
a: 5x + 3 = 4x + 9 because if lines are parallel, then alternate interior angles are equal, x
111
6-34.
Reasoning can vary. See sample responses below.
a: a = 123°, when lines are // , corr. ∠s are =, b = 123°, when lines are // , alt. int. ∠s are =,
c = 57°, suppl. ∠s
b: all = 98°, suppl. ∠s, then when lines are // , alt. int. ∠s = and corres. or vert. ∠s =
c: g = h = 75°, when lines are // , alt. int. or corres. ∠s =, then vert. ∠s = 6-35. a:
Similar (SSS ~) b: Similar (AA ~) 6-36. a: x = !4 and y = 0 b: No solution; the lines
are parallel.
6-37.
4
5
=,
x+ 5
10
x = 7.5
6-38. Let B represent the measure of angle B. Then (3B + 5º) + B +(B – 20º) = 180º, so
m∠A = 122º, m∠B = 39º, and m∠C = 19º.
parentsniece boyfriend
6-39. a: See possible area model at right.
1
1
1
1
1
b: c:
4 9 + 6 + 6 + 4 = 36 ! 69%
3
36 2
25
1
parent
s
6-4.
b: Vertical angles.
niec
e 1
6-40
.
C
a: Alternate interior angles.
c: ∠u & ∠z,
6
∠s & ∠x,
boyfrien
d 1
2
6-5.
a: They are similar by SAS
b: Yes, because they are sim
6-6.
3x +1° + 52° = 180° , x = 127
6-7.
a: 8 cm
b: ≈ 14.97 ft
6-8.
1a and 1b: statements ii and
cupcakes because they are b
6-9.
6-1
0.
6-2
3.
a: 34 or 75%
c: 1 or 100%
b: 3
c: (
A
a: Not similar because there
b: Similar (AA ~)
6-2
4.
a: y = 52 x ! 8
6-2
5.
6-2
b: 1422 = 10 DE , DE ≈
15.71
a: Yes because of AAS ≅ or
6-46. Justifications and order may vary: a = 53° , given; b = 55°, straight angle (with ∠g); c = 72° ,
triangle angle sum; d = 53° , when lines are parallel, alternate interior angles are equal; e = 55° ,
when lines are parallel, alternate interior angles are equal; f = 127° ,straight angle (with ∠a), so they
are supplementary.
2
6-47. a: For left-hand triangle: c = 9+ 36! 2·3·6cos60
! 5.196
units; For
right-hand
33
2
b: Yes; by SSS ≅ or SAS ≅.
triangle: c
= 36+ 27!
a: Converse: If the ground is wet, then it is raining. Not always2·6·3
true. 3
cos30° , c =
b: Converse: If a polygon is a rectangle, then it is a square. Not always true.
3 units;
They areNot always true.
c: Converse: If a polygon has four 90° angles, then it is a rectangle.
congruent.
d: Converse: If a polygon is a triangle, then it has three angles. Always true.
°, c =
6-48.
e: Converse: If vertical angles are congruent, then two lines intersect. Always true.
6-49.
x-intercept: (4, 0), y-intercept: (0, 6)
6-50.
1 y = –2 c: 4 d: x = 4
a: y = b:
4
3
6-51.
a: b:
8
"
3
c:
6-52.
2
3
3
1
8
1
8
d: 8 ; sum must be equal to one.
sin 40°= 600 ,h h ≈ 385.67 feet
x ! 45.56
6-55.
a:
b: x ! 10.63 c: x ! 266.49 d: x = 5
6-56.
9 square units; First find AC = 5 and then calculate 2 (5)(3.6), or use BC as the base and
1
1
calculate 2 (2+ 4)(3).
6-57.
a: m = 33 m, n = 36 m
2
2
b: Area (small) = 378 cm , perimeter (small) = 80 cm, area (big) = 850.5 m , and
perimeter (big) = 120 m
6-58.
a: Similar because of AA ~.
b: Neither because angles are not equal.
c: Congruent because of ASA ≅ or AAS ≅. 6-59. a: ≈
71.56° b: y = x + 3 c: (1, 4) 6-60. D
6-62. a: Lines l and m are parallel because alternate interior angles are equal.
b: Line n is perpendicular to line m because w+ k = 180° and if w = k, then each is 90°.
c: No special statements can be made because vertical lines are always equal.
d: Lines l and m cannot be parallel because otherwise z+ k = 180° .
6-63. a: ΔABC ~ ΔDEF (AA ~)
b: ΔMON ≅ΔPQR, (AAS ≅ or ASA ≅)
!
!
!
c: Neither congruent nor similar because m!J " 62 . If m!J = 62 , then m!L = 180 "
!
!
sin56° sin 72°
2#62 = 56 . Since
!
, this triangle cannot
58exist.
6-64. a: Converse: If the cat runs away frightened, then it knocked over the lamp. Not alwaystrue.
1
b: Converse: If the chances of getting a 3 are 6 , then a 6-sided dice was rolled. Not
always true.
c: Converse: If a triangle is a right triangle, then it has a 90° angle. Always true.
6-65.
1
94
6-66. D
!## !##
6-67. a: It is a trapezoid. The slope of WZequals the slope of XY.
b: ≈ 18.3
units
c: (–9, 1)
d: 2
6-73. a: Yes, because parallel lines assure us that the alternate interior angles are congruent.
Since corresponding angles in the triangles have equal measure, the triangles aresimilar by AA ~.
b: 24x, x= x+2
= 10
20
6-74. a: x = 4 b: x = 55°
c: x = 23° and y = 43° d: x = 5.5 and y = 45.2 6-75. P(Aor B)=P(A)+P(B)– P(A and B)= 4% +
1
1
% ! 2 % = 4%. If a refrigerator has a
dent it also always has a paint blemish. 6-76. area ≈
2
100.55 sq. yards;
perimeter ≈
43.36 yards 6-77. a: 288
feet by 256 feet
b: area of shape = 59.5 square units; area of island = 60,928 square feet 6-78. C
Lesson 6.2.4
6-83. a: Congruent (HL ≅ or SAS ≅) b: Congruent (AAS ≅)
c: Not necessarily congruent. d: Congruent (SAS ≅)
6-84. a: x + 4x ! 2°= 90° , x = 18.4, complementary angles
b: 2m + 3°+ m !1°+ m+ 9°= 180° , m = 42.25, Triangle Angle Sum Theorem
c: 7k ! 6°= 3k +18° , k = 6, vertical angles are equal
x
8
d: 16 = 13 , x ! 9.8 , corresponding parts of similar figures have equivalent ratios
6-85. x = 11; m∠ABC = 114º
6-86. a: Converse: If a triangle is isosceles, then its base angles are congruent. Always true.
b: Converse: If the sum of the angles in a figure is 180° , then the figure is a triangle.
Always true.
c: Converse: If my mom is happy, then I cleaned my room. Not always true.
6-87. 36%
6-88. D Selected
Answers
6-4.
a: Alternate interior angles.
b: Vertical angles.
c: ∠u & ∠z,
6-5.
∠s & ∠x,
∠v & ∠w,
and ∠t & ∠y
a: They are similar by SAS ~.
b: Yes, because they are similar and the corresponding sides have a ratio of 1.
6-6.
3x +1° + 52° = 180° , x = 1273 ! 42.33°
6-7.
a: 8 cm
b: ≈ 14.97 ft
c: ≈ 15.2 in.
6-8.
1a and 1b: statements ii and iv, 2: The cupcakes are burned, 3: The fans will not buy the
cupcakes because they are burned, 4: The team will not have enough money for uniforms.
6-9.
6-1
0.
6-2
3.
6-2
4.
6-2
5.
6-2
6.
6-2
7.
6-2
8.
19
118
16
a: 34 or 75%
c: 1 or 100%
b: 320 or 15%
c: (b) is an intersection, and (c) is a union.
A
a: Not similar because there are not three pairs of corresponding angles that arecongruent.
b: Similar (AA ~)
a: y = 52 x ! 8
b: y = 32 x +1
b: 1422 = 10 DE , DE ≈
15.71
a: Yes because of AAS ≅ or ASA ≅; ΔDEF ≅ ΔLJK. b: One possible answer, a
reflection across line segment JK and then a translation of ΔDEF to line up point J and
point E, followed by a rotation. c: KL ≈ 4.3 units
c = 10 by substitution.
a: P(A or B) = P(A) + P(B) – P(A and B) = 64212 + 112212 ! 0 = 176212 " 83.0% ; the
probability of A and B (the overlap) was 0. b: P(A or B) = P(A) + P(B) – P(A and B) !
75%= 114212 + 56212 ! x " x # 5.1%
11
8
16
13
6
11
2
11
2
14
a: 5x + 3 = 4x + 9 because if lines are parallel, then alternate interior angles are equal, x