r-N,
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-----.a.
1
i
I NAME
DATE
,
rPra ctice Worksheet
-
Parallelograms
fhe figure at the right is a parallelogram, Use this tigure and
the information given to solve each problem.
1. If nZ.BCD
- L25, flnd mlBAD.
2. lf nZBAC = 45,findmlACD.
3. If wIBEA = 135, find n/.AED.
4. If nZ.ABC - 50, find mlBCD.
5. If AB-5x-3and CD=2x+9,frndAB.
6. lf nZDAB = 2x findmlDAB.
7. It wIBAD
= 3x
10 and
wZADC
- 3x,
- 12 and
nIBCD=x+40,findnZBAD.
l-\-
Write a two-column proof.
8. Given: ABCD ts a parallelogram,
BE =AD
Prove: Zl = /.C
37
Glencoe Division, Macmillan/McGraw-Hill
,,-\-
-
I
/
.r
I NAME
DATE
ctice Worksheet
-g!Pra
Parallelograms
The figure at the right is a parallelogram. Use this figure and
the information given to solve each problem,
l.
If nIBCD = 125, find mlBAD. 125
2. If TnZBAC = 45,find.nZ.ACD. 45
3. If nZBEA -
135, find.mtAED.
45
4. lf nZ.ABC = 50,find.mZBCD. 130
5. If AB = 5x -3
and CD = 2x + 9,findAB.
17
6. If m/.DAB = 2x - 10 and wIADC = 3x,
find.mZDAB. 66
7. If wZBAD = 3x - 12 and
rnlBCD = )c + 40, frnd mlBAD. 66
Write a two-column proof.
8. Given: ABCD
ts a parallelogram,
BE =AD
Prove: lI
=
lC
Statements
Reason
a. ABCD is a
a. Given
parallelogram.
b. AD= BC
-B-EFM
BC=
BE
e.
21 =ZC
b. Opposite sides of a parrallelogram
are congruent.
c. Given
d. Congruence of segments is
transitive.
e. lf two sides of a triangle are
congruent, then the angles opposite
those sides are congruent.
T37
Glencoe Division, Macmillan/McGraw-Hill
-
'dpl;
DATE
ctice Worksheet
Problem-Solving Strategy: Look for a Pattern
6olve.
1.
Use any strategY'
for a ping pong singles
play,
the looser is eliminated
people
tournament. After two
TWo hundred people signed up
fromthecompetition.Howmanymatcheswil1therebe
before a winner can be determined?
2.
How many squares are there in the figure shown at the
right? (Hint: There are more than 16.)'
3. Find the sum of the first
L,1,2,3, 5,8, 13, . . .
20 terms of the following sequence:
4. Tanya likes to burn candles. She has found that,
once a
candle has burned, she can melt 3 candle stubs, add a new
wick, and have one more candle to burn. How many candles
total can she burn from a box of 15 candles?
5. In a college senior class I of t;,,e young men are engaged to
consists
f of the women. What fraction of the senior class
of women.
38
Glencoe Division, Macmillan/McGraw-Hill
NAME
-W
DATE
Practice Worksheet
Problem-Solving Strategy: Look for a Pattern
Solve. Use any strategy.
1.
TWo hundred people signed up for a ping pong singles
tournament. After two people play, the looser is eliminated
from the competition. How many matches will there be
before a winner can be determined? 199
2.
How many squares are there in the figure shown at the
right? (Hint: There are more than 16.) 30
3. Find the sum of the first 20 terms
I,1,2,3,5,8, 13,.. " 171710
4.
of the following sequence:
Tanya likes to burn candles. She has found that, once a
candle has burned, she can melt 3 candle stubs, add a new
wick, and have one more candle to burn. How many candles
total can she burn from a box of 15 candles? 22
5. I"
a college senior class I of theyoung men are engaged to
f of the women. What fraction of the senior class consists
of women.
10
17
T38
Glencoe Division, Macmillan/McGraw-Hill
dl
I
''----o-o 'Pra ctice Worksheet
/al
INAME
DATE
Iesfs for Parallelograms
What values must x and y have in order for each quadrilateral
to be a parallelogram?
1.
3.
Refer to the figure at the right.
-YZ bisects IWK and
ZK bisect s IZLM. Also,
lI = 12.
Is YZLK a parallelogram?
Explain.
4.
Refer to the figure at the right.
AC = WV and' 3P = WV.
Also, AB =XY and gP = xY.
Is ABCD a parallelogram?
Explain.
Determine whether ABCD is a parallelogram given each
set of vertices. ExPlain.
5. A(2,5), B(5,9), c(3, -1), D(6, 3)
6. A(-1, 6), B(2, -3), C(5, 9), D(2,7)
39
Glencoe Division, Macmillan/McGraw-Hill
- .'-
. ., lrot,
'.l o-J
---------
DATE
Pra ctice Worksheet
Iesfs for Parallelograms
What values must x and y have in order for each quadrilateral
to be a parallelogram?
1.
any values for x
and y that are
greater than 0
3. Refer to the figure at the right.
YZ bisects
LKbisects
/-I = /2.
IXYK and
IZLM. Also,
)
Is YZLK a parallelogram?
Explain.
yes; Opposite angles are congruent.
4, Refer to the figure at the right.
AC = WV and BD = WV.
Also, AB = XY and, CO = XY.
Is ABCD a parallelogram?
Explain.
yes; Both pairs of opposite
sides are congruent.
Determine whether ABCD is a parallelogram given each
set of vertices. Explain.
5. A(2,5),I'fo, g), C(3,-1), D(6, 3)
yes; Opposite sides have equal lengths and are therefore
congruent.
6. A(-L,6), B(2, -3), C(5, g), D(2,7)
no; Slope AD- lrand stope
BC= 4, so these two opposite
sides are not parallel.
T39
Glencoe Division, Macmillan/McGraw-Hill
4t I 6-!)Pra
ctice Worksheet
*---=
I NAME
DATE
Rectangles
lJse rectangles ABCD and the given information
to solve each
problem.
l.
ItAC
=
4x-
60 and BD =
30-r,
frndBD.
A
IflAC = 4x -60 and AE = x + 5, find EC.
If ruIBAC = 4x + 5 and nZCAD
findmlCAD.
= 5x
-
14,
4. If AE -- 2x + 3 and BE = 12 - x, frnd BD.
5. nZBAC = 3x + 5 and n/ACD
FindnZAED.
= 40
- 2x.
Determine whether PQRS is a rectangle. Explain.
6.P(2,3), @(5, 9),,R(11, 6), S(8,0)
7. P(-L,4), Q(3,6), R(9, -3), S(5, -5)
g. P(1, 3), 8(4,
7), R(6, 2), S(2, 4)
g. P(-1, -3), 8(-4,
6), R(8, 1o), S(11, 1)
10. P(-1, -2), Q(5, 2), R(13,-10), S(7, -14)
40
Glencoe Division, Macmillan/McGraw-Hill
^'^'/
I
I NAME
gPractice
DATE
Worksheet
Rectangles
Use rectangles ABCD and the given information to solve each
problem.
l.
If AC
- bc- 60 and BD = 30-r, findBD.
A
12
2. If AC - bc -60
40
3. If wIBAC
and AE = x + 5,find EC.
= 4x + 5 and
wICAD
findnZCAD.
41
4. If AE =2x + 3 and BE =
t2-x,
= 5x
- L4,
D
frndBD.
18
5. nIBAC
= 3x + 5 and m/ACD = 40 - 2x.
Find nZAED.
52
Determine whether PQRS is a rectangle. Explain.
6.P(2,3), @(5, g),8(11, 6), S(8,0)
yes; opposite sides parallel and all right angles
7. P(-r,4), Q(3,6), R(9, -3), S(5, -5)
no; not all right angles
g. P(1, 3), Q(4,7), R(6,2), S(2, 4)
no; opposite sides not parallel
g. P(-1, -3),QG4,6),R(8, 10), S(11, 1)
yes; opposite sides parallel and all right angles
10. P(-1, -2), Q(5,2), R(r3., -10), S(7, -L4)
yes; opposite sides parallel and all right angles
T40
Glencoe Division, Macmillan/McGraw-Hill
dl
I
7t-l
I NAME
r---_o-e J Pra ctice Worksheet
DATE
Squares and Rhombi
Jse square ABCD and the given information to solve each
problem.
l.
If wZAEB = Stc, fi.nd r.
2. lf nIBAC
= 9x, frnd
r.
S. lf AB = 2x +4 and CD = 3x - 5,find BC.
4. lf m/.DAC
=
5. It AB = x2 -
! andmlBAC = 3x, frnd r.
15 and BC = 2x, ftnd x.
Ilse rhombus ABCD
each measure.
and
the
given information to find
6. mtBCE
B
7. nZBEC
59"
8. AC
9. nIABD
14 cm
D
LO. AD
Determine whether EFGH is a parallelogram, rectangle,
rhombus, or square. List allthat apply.
11. .E(0, -3), .F'(-3, 0), G(0, 3), F(3, 0)
12. E(2,1), tr'(3, 4),
G(7
,2), H(6,
-r)
41
Glencoe Division, Macmillan/McGraw-Hill
-NI
tt
. !-
o-c
------
DATE
INAME
Pra ctice Worksheet
Squares and Rhombi
Use square ABCD and the given information to solve each
problem.
l.
- 3x, findr. 30
If n/.AEB
2. If wZBAC =9x, findr. 5
3. IfAB = 2x +4 and CD = 3x - 5, find BC. 22
4, If nZDAC
5.
If AB = x2
=
!
and,
r. 15
wIBAC = 3x, find
- 15 and BC = 2x, f:rnd. x. 5
lkse rhombus ABCD antd the given information to find
each measure.
6. mzBCE 31
B
7. mtBEC 90
59"
t2
8. AC 24 Cm
14 cm
9. mtABD 56
D
to. AD 14 cm
Determine whether EFGH is a parallelogram, rectangle,
rhombus, or square, List all that apply.
tt..
E(0, -3), F'(-3, 0), G(0, 3), F(3, 0)
parallelogram, rectangle, rhombus, square
12. E(2,1), F'(3, 4), G(7,2), H(6,
parallelogram
Gm
-l)
,
T41
Glencoe Division, Macmillan/McGraw-Hill
wlr/l
I
i"--r--o
I
11 --r
DATE
NAME
Pra ctice Worksheet
Trapezoids
For Exercises 1-7, refer to the figure, MATH is anisosceles
trapezoid with bases tna and TH. llse the figure and the given
information to solve each problem.
l.
If MA = 34 and HT = 20, find CD.
2. If Hf = 17.6 and, CD -
28.6, find, MA.
s. If MA = 23.9 and, AD -
L6.4, find, HT.
4. lf CD=x+12andMA+nf =4x+ 3,findr.
5. lf mzTAM 6. lf wZHCD
63, findmZHMA.
- l2,findmlTDC.
7. If wZDCM = 2x, ftnd wZCMA in terms
of r.
8. If the measure
of the median of an isosceles trapezoid is 5.5,
possible
integral measures for the bases?
what are the
9.
WV is the median of a trapezoid that has bases MN andPO,
with V on OM and W on PN. If the vertices of the trapezoid
are M(2,6), N(4, 6) P(10, 0), and O(0, 0), frnd the coordinates
ofVand W
lO. WV is the median of a trapezoid that has bases MN andPO,
with V onPM and W on ON. If four of the points are
M(5,I0),M9,
10), V(3,7), and
coordinates of P and O.
l(11,
7), find the
42
Glencoe Division, Macmillan/McGraw-Hill
& IgPractice
DATE
INAME
Worksheet
Trapezoids
For Exercises 1-7, refer to the figure. MATH is an isosceles
trapezoid with bases MA and TH. Use the figure and the given
information to solve each problem.
l.
If MA = 34 and HT = 20,
2. If nT =
17.6 and CD
3, lt MA = 23.9
and,
eD
find.
TD. 27
=
28.6, find MA.
39'6
-
16.4, find, HT.
8.9
4. If CV = x + 12 and. MA
+
nf
= 4x + 3, frnd
r.
10.5
5. If nITAM - 63, find wZ.HMA. 63
6. If nZHCD
-
52,flnd,IZTDC. 52
7. If nIDCM - 2x, find, wICMA in terms
of
r. 180 - 2X
of the median of an isosceles trapezoid is 5.5,
what are the possible integral measures for the bases?
8. If the measure
1,10;2,9;3,8; 4,7;5,6
g.
W
is the median of a trapezoid that has bases M-N andPO,
with V on OM and W on PN. If the vertices of the trapezoid
are M(2,6), N(4, 6) P(10, 0), and O(0, 0), frnd the coordinates
of V and w. V(l , 3), W(7 , 3)
L0, WV is the median of a trapezoid that has bases MN and PO,
with V onPM and W'on ON. If four of the points are
M(5,I0), M9, 10), V(3,7), and W(11, 7),-frnd-the
coordinates of P and O. P(l, 4), O(13' 4)
T42
Glencoe Division, MacmillanlMcGraw-Hill