b:
Not possible.
Same-side interior angles should add up to 180° or, the sides are not
parallel.
c:
Not possible.
One pair of alternate interior angles are equal, but the other is not for the
same pair of lines cut by a transversal; or, the vertical angles are not equal.

Selected Answers
© 2006 - 2016 CPM Educational Program.
All rights reserved.
11
Lesson 6.2.1
6-53.
a
: R
b:
I
c:
I
d:
R
6-54.
D
6-55.
a:
12 + 13
i
b:
21 – 10
i
c:
–80
d:
2
6-56.
x
=
8
2
≈
11.3
units;
Methods include using the Pythagorean Theorem to set up the
equation
x
2
+
x
2
= 16
2
, using the 45°- 45°- 90° triangle pattern to divide 16 by
√
2, or
using sine or cosine to solve.
6-57.
a:
x
= 8, –13
b:
x
=
14
3
,
−
10
3
c:
x
=
17
2
,
−
11
6-58.
a:
See diagram at right.
b:
Since corresponding parts of congruent
triangles are congruent, 2
y
+ 7 = 21 and
y
= 7.
Lesson 6.2.2
6-62.
a:
(5
1/2
)
6
= 5
3
= 125
b:
7
5
= 16807
c:
(81
3
)
1/4
= 81
3/4
= (81
1/4
)
3
= 3
3
= 27
6-63.
a:
P = 2
10
+ 34
≈
40.3 mm, A = 72 sq mm
b:
P = 30 feet, A = 36 square feet
6-64.
10.1% by using the Addition Rule.
6-65.
a:
y
=
ax
(
x –
5)
b:
y
=
a
(
x
– 6)(
x
+ 6)
c:
y
=
a
(
x
+ 0.25)(
x
– 0.75)
6-66.
x
= 11º;
m
∠
ABC
= 114º
6-67.
A
(2, 4),
B
(6, 2),
C
(4, 5)
T
A
P
14
18
21
D
O
G
2
y
+ 7

12
© 2006 - 2016 CPM Educational Program.
All rights reserved.
Core Connections Integrated II
Lesson 6.2.3
6-73.
≈
36.4 feet from the point on the street closest to the art museum.
6-74.
a:
w
=
±
17
5
≈
±
1.84
b:
w
=
3
±
349
10
w
≈
2.17 and –1.57
c:
w
=
±
i
3
≈
±
1.73
i
6-75.
a:
real
b:
complex
c:
complex
d:
real
e:
real
f:
complex
6-76.
a:
P
= 23.4 m;
A
= 10.5 m
2
b:
P
= 70.2 m;
A
= 94.5 m
2
c:
yes
d:
The perimeter triples,
but the area increases
by a factor of 9.
6-77.
sin
−
1 7
8
≈
61º
6-78.
See tree diagram at
right (an area model is
not practical).
P
(three
yogurts) = 12.5%.
100%
−
12.5% = 87.5%
chance of
not
getting
three yogurts.
yogurt
green
apple
red
apple
yogurt
green apple
red apple
yogurt
green apple
red apple
yogurt
green apple
red apple
yogurt
green apple
red apple
= 12.5%
yogurt
green apple
red apple
yogurt
green apple
red apple
yogurt
green apple
red apple
yogurt
green apple
red apple
yogurt
green apple
red apple
yogurt
green apple
red apple
yogurt
green apple
red apple
yogurt
green apple
red apple

Selected Answers
© 2006 - 2016 CPM Educational Program.
All rights reserved.
13
Lesson 6.2.4
6-84. a:
x
=
1
5
or –3
b:
x
=
1
2
or –3
c:
x
=
−
1
±
2
i
d:
x
= –7 or 2
6-85. a:
16
b:
3125
c:
2187
6-86. a:
(0, –9);
It is the constant term in the equation.
b:
(3, 0) and (–3, 0);
Notice that the product of the
x-
intercepts equals
the constant term.
6-87.
AB
≈
11.47 units,
A
≈
97.47 sq. units
6-88.
The triangles described in (a), (b), and (d) are isosceles.
6-89.
E
Lesson 6.2.5
6-91.
area
≈
100.6 sq. yards;
perimeter
≈
43.4 yards
6-92.
a:
x
=
1
4
b:
x
=
−
1
±
i
3
2
6-93.
No, there are several problems with her diagram.
The sum of the lengths of the two
shorter sides of the triangle is less than 15, so the three sides would not form a triangle.
Also, 22º > 18º, but 5 ft < 8 ft, so the larger angle is not opposite the longer side.
6-94.
a:
It is a parallelogram, because
MN
||
PQ
and
NP
||
MQ
.
b:
(1, –5), a reflection across the
x
-axis.
6-95.
a:
f
(
t
) = 135000(1.04)
t
, 135000 is the initial value at time 0 and 1.04 is the multiplier for
an increase of 4% each year. (100% + 4% = 104%, or 1.04.)
b:
≈
$199,833
6-96.
C
x
y

14
© 2006 - 2016 CPM Educational Program.
All rights reserved.
Core Connections Integrated II
Lesson 6.2.6
6-101. a:
1
b:
20
x
c:
5
t
3
d:
x
2
y
6-102. a:
(
i
−
3)
2
=
i
2
−
6
i
+ 9 =
−
1
−
6
i
+ 9 = 8
−
6
i
b:
(2
i
−
1)(3
i
+ 1) = 6
i
2
−
3
i
+ 2

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- Winter '16
- Mr. Snyder
- Pythagorean Theorem, triangle, 20a3b