1. No category

Name
Class
Date
Extra Practice
Chapter 6
Lesson 6-1
Find the sum of the interior angle measures of each polygon.
1. octagon 1080
2. 16-gon 2520
3. 42-gon 7200
Find the missing angle measures.
4.
5.
106°
( x15)°
94°
135°
70°
x°
x 100; (x 5) 105
6.
z°
x°
x°
x°
(x26)°
78°
90° y°
x°
x°
x 122; (x 6) 116
x 110; y 102; z 82
Find the measure of one interior angle and the measure of one exterior angle in
each regular polygon.
7. nonagon interior: 140,
exterior: 40
8. 20-gon interior: 162,
exterior: 18
9. 45-gon interior: 172,
exterior: 8
Lesson 6-2
Find the values of the variables in each parallelogram.
10. y°
11.
x 12;
y 84
7x°
8x°
13.
(2x15)°
(2y15)°
14.
2y29
3x11
5x21
(4x25)°
(y110)°
(7y21)°
(3x126)°
4x°
(5y121)°
12.
y
15.
x 8;
y 25
5x
3y18
5y
x18
2x24
x 1; y 7
16. Given: PQRS and QDCA
y1
15
x 30;
y 55
x 26; y 11
y22
3x11
x 12;
y4
17. Given: ^ABCD
M is the midpoint of CD.
Prove: PM AD
are parallelograms.
Prove: AP BS
D Since
B
C
PQRS is
The
a ^, its
diagonals of
P
M
opp. sides
a ^ bisect
A
C
B
are , so
each other,
PA SB and PS QR. Since
so P is the
S
P
D
QDCA is a ^, AB QR. Thus, A
midpt. of AC.
PS AB because two lines to the same line
P and M are midpts. of two sides of
are . PABS is a ^ by def. of ^, and AP BS
NACD so, by the N Midseg. Thm.,
since opp. sides of a ^ are .
PM AD.
Q
R
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Name
Class
Date
Extra Practice (continued)
Chapter 6
A
18. In the figure, BD DF . Find DG and EG.
DG 3.2; EG 2.05
B
3.2
C
2.05
D
E
F
Lesson 6-3
G
Based on the markings, decide whether each figure must be a parallelogram.
19.
20.
21.
yes
yes
22.
23.
no
24.
yes
yes
no
25. Describe how you can use what you know about Sample answer: Mark two segments
parallelograms to construct a point halfway on each of the two lines. The two
segments are opposite sides of a ^. Construct
between a given pair of parallel lines. (draw) the diagonals of the ^. The diagonals
intersect at their midpts., which is the desired point halfway between the lines.
26. Given: ^ABCD
B
BX AC, DY AC
Prove: BXDY is a
parallelogram.
C
Y
X
A
D
Lessons 6-4 and 6-5
ABCD is a ^ (given), so ABDC and
AB DC . BAX DCY by the Alt.
Int. Thm. AXB and CYD are rt.
and therefore . NAXB NCYD
by AAS and BX DY by CPCTC.
Since BX AC and DY AC (given),
BX DY . BXDY has a pair of sides and , so BXDY is a ^.
For each parallelogram, determine the most precise name and find the
measures of the numbered angles.
27.
1
2
square;
m1 45;
m2 45
28.
4
2 3
1
50°
30.
3
116°
2
1
4 rectangle;
m1
m2
m3
m4
31.
4
rhombus;
m1 50;
m2 90;
m3 40;
m4 40
29.
2
3 ^;
55°
80°
32.
2
1
116;
27°
64;
3
32;
58
rhombus; m1 90; m2 27;
m3 63; m4 63
1
4
3
2
40°
4
1
m1
m2
m3
m4
45;
45;
80;
55
rectangle;
m1 40;
m2 100;
m3 50;
m4 80
1SFOUJDF)BMM(FPNFUSZ t Extra Practice
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Name
Class
Date
Extra Practice (continued)
Chapter 6
33. Use the information in the figure.
34. ^ABCD is a rhombus. What is
Explain how you know that ABCD
is a rectangle.
the relationship between 1 and 2?
Explain.
1 and 2 are
B By the Conv.
of the Isos. N
P
Thm. and given
that PA PB,
D
C it follows that
PD PA PB PC . Thus, the diagonals of ABCD A
bisect each other (so ABCD is a ^) and are (by
the Seg. Add. Post.), so ABCD is a rectangle.
A
B
C compl. The diags.
of rhombus ABCD
are and bisect
each other so the 4
small Ns are rt.
Ns. 1 and CBK
are compl., and
CBK 2, so 1
and 2 are compl.
1
K
2
D
What value of x makes each figure the given special parallelogram?
35. rhombus
36. rectangle
(5x215)°
37. rhombus
5x2
3
3x 1
(4x11)°
11
(4x15)°
x7
x 16
(7x23)°
x8
Lesson 6-6
Find m1 and m2 .
38.
39.
1
m1 110,
m2 25
2
110°
67°
40.
2
1 53°
m1 90,
m2 23
1
2
m1 45,
m2 74
41.
42.
1
2
2
43.
1
m1 110,
m2 70
70°
m1 70,
m2 70
110°
2
m1 74,
m2 106
1
74°
B
C
44. Suppose you manipulate the figure so that NPAB,
NPBC, and NPCD are congruent isosceles triangles
with their vertex angles at point P. What kind of figure A
is ABCD? Be sure to consider all the possibilities.
D
ABCD is an isos. trap. except when mAPB 90 , and in
that case it is a square.
P
Find EF in each trapezoid.
45.
A
E
B
x11
3x22
10
D
EF 7
F
46.
E
C
4
A
B
x15
4x12
47.
EF 7
D
A
F
C
E
B
x22
x13
2x
D
EF 11
F
C
1SFOUJDF)BMM(FPNFUSZ t Extra Practice
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Name
Class
Date
Extra Practice (continued)
Chapter 6
Lesson 6-7
Graph the given points. Use slope and the Distance Formula to determine the
most precise name for quadrilateral ABCD.
48. A(3, 5), B(6, 5), C(2, 1), D(1, 3)
6
4
y
A
49. A(1, 1), B(3, 1), C(1, 3), D(5, 1)
y
A
x
4 rhombus
22 O
D
B
22
B
trapezoid
D
2
O
2
O
x
C
4
C
6
Lesson 6-8
Give coordinates for points D and S without using any new variables.
50. parallelogram
y (c1a, b)
D
51. rhombus
y
(0, b)
x
x
D
S
(c, 0)
D(0, b); S(a, 0)
Lesson 6-9
52. isosceles trapezoid
y
D
(a, c)
x
(c, 0)
S
(2b, 0)
S
D(a, c); S(b, 0)
D(c, 0); S(0, b)
53. A square has vertices at (2a, 0), (0, 2a), (2a, 0), and (0, 2a).
D(0, 2a) y
N(2a, a)
Use coordinate geometry to prove that the midpoints of
the sides of a square determine the square.
Q(22a, 0)
Given: Square DRSQ with K, L, M, N midpts. of DR,
RS , SQ and QD, respectively.
Prove: KLMN is a square. K(a, a), L(a, a), M(a, a),
and N(a, a) are midpts. of the sides of the square.
KL LM MN NK 2a. The slopes of KL and MN
are undefined. The slopes of LM and NK are 0, so adj.
sides are to each other. Since all are rt. , the quad.
is a rectang. A rectang with all sides is a square.
K(a, a)
x
O
R(2a, 0)
L(a, 2a)
M(2a, 2a)
S(0, 22a)
y
54. In the figure, NPQR is an isosceles triangle. Points
M and N are the midpoints of PQ and PR, respectively.
Give a coordinate proof that the medians of isosceles
2b
triangle PQR intersect at H ;0, 3 < .
P ( 0 , 2b)
M
N
H(0, 2 b )
3
x
Q(22a, 0)
R(2 a, 0)
b
The line through R(2a, 0) and M(a, b) is y 3a
(x 2a).
b
The line through Q(2a, 0) and N(a, b) is y 3a(x 2a). For each line, when x 0,
2b
y 2b
3 , so the three medians all contain point H ;0, 3 <.
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