Download Chap 6 homework packet

Homework Worksheets: Chapter 6
HW#30: Problems #1 – 11
1.) All of the following statements are true except:
A.
B.
C.
D.
E.
Opposite sides of a parallelogram are congruent.
Opposite angles of a parallelogram are congruent.
Diagonals of a parallelogram are congruent.
Diagonals of a parallelogram bisect each other.
Opposite sides of a parallelogram are parallel.
3.) Quadrilateral ABCD is a parallelogram. Which of
the following must be true?
A.
B.
C.
D.
E.
AB = BC
BC = CD
mA  mD
AC = BD
D  B
2.) A regular polygon has 10 sides. Find the
measure of each interior angle.
A.
B.
C.
D.
E.
4.) The measure of an exterior angle of a
regular polygon is 18˚. Find the measure of
each interior angle.
A.
B.
C.
D.
E.
5.) Identify a counterexample to the given statement:
360˚
36˚
1440˚
144˚
180˚
18˚
162˚
180˚
360˚
3240˚
6.) Scalene triangles have ______ congruent
sides.
Two planes always intersect at a line.
A.
B.
C.
D.
E.
No counterexample needed; this is true.
Two perpendicular lines.
Two parallel lines.
Two intersecting planes.
Two parallel planes.
7.) Simplify each expression:
a) 3 24
b) 5 2  2 42
 6 
c) 

 2
2
d)
6 3
5 2
A.
B.
C.
D.
E.
0
1
2
3
not enough information to conclude
8.) Simplify each expression:
a) 6 96
b) 4 8  3 6
c)
12
3
d)
6 7 
2
For #9-11, solve each equation by factoring:
9.) 8 x 2  6 x  5  0
10.) 6 x 2  19 x  3
11.) 12x3 – 75x = 0
HW #31: Problems #12-24
Quadrilateral MNOP is a parallelogram.
N
O
P
M
12.) Name the property of parallelograms that
justifies the statement:
MN = OP
(Diagram for #13-14)
13.) Name the property of parallelograms that
justifies the statement: N  P
A. Opposite sides of a parallelogram are congruent.
B. Opposite angles of a parallelogram are
congruent.
C. Diagonals of a parallelogram bisect each other.
D. Opposite sides of a parallelogram are parallel.
E. Consecutive sides of a parallelogram are
congruent.
14.) Name the property of parallelograms that
MN PO
justifies the statement:
A. Opposite sides of a parallelogram are
congruent.
B. Opposite angles of a parallelogram are
congruent.
C. Diagonals of a parallelogram bisect each other.
D. Opposite sides of a parallelogram are parallel.
E. Consecutive sides of a parallelogram are
congruent.
A. Opposite sides of a parallelogram are congruent.
B. Opposite angles of a parallelogram are
congruent.
C. Diagonals of a parallelogram bisect each other.
D. Opposite sides of a parallelogram are parallel.
E. Consecutive sides of a parallelogram are
congruent.
15.) Find each quantity for a regular decagon:
16.) All of the following information is enough to
state that a quadrilateral is a parallelogram except:
Sum of Exterior Angles:
Each Exterior Angle:
Each Interior Angle:
Sum of Interior Angles:
17.) Solve for x by factoring:
2x2 – 6 = -x
A. Both pairs of opposite sides are congruent.
B. Both pairs of opposite angles are congruent.
C. One pair of opposite sides of is both congruent
and parallel.
D. One pair of opposite sides is parallel, the other
pair of opposite sides is congruent.
E. Both pairs of opposite sides are parallel.
18.) Solve for x by factoring:
16x3 – 12x2 = 18x
19.) Solve for x:
x2 + x2 = 62
19.) Solve for x:
(2x)2 + x2 =  5 5  2
20.) Find the equation of the line
that passes through (-3, 4) and
(8, 1) in standard form.
For #22-24, a trapezoid and its median are shown. Solve for x.
22.)
23.)
25
x
13
x
13
21
21.) Find the equation of the
line in slope-intercept form that
passes through (2, 5) and is
parallel to y = 2x + 1
24.)
3x + 2
2x + 4
2x + 1
HW #32: Problems #25 – 33
25.) In the figure below, AC  DF , A  D .
F
C
A
B
D
26.) Identify a counterexample to the following
statement:
If one pair of opposite sides of a quadrilateral is
parallel, then the quadrilateral is a
parallelogram.
E
Which addition information would be enough to
prove that ABC  DEF ?
A. AB  DE
C. BC  EF
E. AB  BC
A.
B.
C.
D.
E.
B. AB  BC
D. BC  DE
27.) All of the following are examples of
parallelograms except:
A. rhombus
C. square
E. none of the above
32.) Simplify:
4  48
a)
6
28.) The measure of each interior angle of a
regular polygon is 140˚. What kind of polygon
is it?
B. trapezoid
D. rectangle
29.) Solve by factoring:
3x2 – 5x = 2
rectangle
rhombus
square
trapezoid
parallelogram
A. a regular pentagon
C. a regular octagon
E. a regular decagon
30.) Solve:


B. a regular hexagon
D. a regular nonagon
31.) Find the equation of the
line passing through (6, -2) and
perpendicular to y = 3x – 5.
2
x2 + 2 34 = (3x)2
33.) Simplify:
b)
6  40
2
6  (6)2  (4)(1)(16)
4
HW#33: Problems #34-44
34.) The perimeter of PQRS is 22in.
QR is 3in longer than RS. Find QR and RS.
35.) Quadrilateral ABCD is a parallelogram. If
adjacent angles are congruent, ABCD must be
________________.
A. a square
B. a rhombus
C. a rectangle
D. a trapezoid
E. equilateral
For questions #36-37, solve by factoring.
36.) 8x3 + 4x2 = 84x
37.) 18 x 2  9 x  20  0
For questions #38-39, simplify:
38.) 5 12 3 30



39.)
5  (5)2  (4)(1)(6)
2
For #40-42, a trapezoid and its median are shown. Solve for x.
40.)
41.)
42.)
4x + 3
x+ 5
2x + 1
2x
3x + 2
x- 4
2x - 2
5x - 10
x+ 4
For 43-44, write the equation of each line described.
43.) Write the equation of the line in slope44.) Write the equation of the line in standard
intercept form that passes through the points
form whose x-intercept is -4 and whose y(-1, 6) and (-2, 4).
intercept is 3.
HW #35: Problems #45-56
45.)
ABC is equilateral. If mA  2 x  y and
mB  4 x  y , solve for x and y.
46.) The measure of an exterior angle of a regular
polygon is 60˚. What is the sum of the measures of
the interior angles?
A.
B.
C.
D.
E.
120˚
180˚
360˚
540˚
720˚
For #47-52, write the letter of every special quadrilateral that has the given property.
A Parallelogram
B Rectangle
C Rhombus
D Square
E Trapezoid
47.) two pairs of adjacent sides
are congruent
48.) diagonals are perpendicular
49.) opposite angles are
congruent
50.) diagonals are congruent
51.) two pairs of opposite sides
are parallel
52.) all angles are right angles
For 53-56, write the equation of each line described.
53.) The line passes through the point (-6, -2)
54.) The line passes through the point (8, -1) and is
and is perpendicular to the line whose equation is parallel to the line whose equation is
3x + 2y = 8.
5x – 4y = 6.
55.) The line is parallel to the line 2x – 4y = 12
and passes through the point (-6, -8).
56.) The line is perpendicular to the line whose
equation is 4x - 8y = 24 and passes through the
point (-2, 8).