Download FOR USE WITH SECTION 5.6

DAÏE
FOR USE WITH SECTION 5.6
1. All of the faces of this prism
a.
are rectangles.
Explain how you know that MW is perpendicular to plane WXYZ.
b. Explain how
to show that IufWllNX.
Sketch each situation.
2. Plane C is parallel to plane D.
3. In plane E, lines m
and
n are parallel. Line p is perpendicular to plane
E.
4. In plane F, lines a and b intersect in point rR and line c is perpendicular to
plane F at point R.
In the diagram, plane B ll plane C.
5. How ne XY
and WT related? Explain how you know.
6. What type of quadrilateral is XYZW?
7.
Suppose
nLXYZ = 54". Find wLWZY.
8. Name two angles that are congruent to LXYZ.
f
n the diagram at
9. How
the right, laces AEHD and
are edges
BFGC
lie in parallel planes.
AE and BF rcIated? Explain how you know.
1O. Find the value of each variable,
if
possible.
If it is not possible, explain
why not.
L7..ln the diagram at the right, PT Lplane QRS.
a. Find wLPTQ.
b. Find
nLPQT.
c. Find nLPRT.
d. Find nLPST.
e.
36
If wLQTR = 90" and QT =
TR, find
wLTQR and wLTRQ.
Practlce Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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NAME
1,.
Draw
DATE
a
horizontal segment CD and construct its perpendicular bisector.
3. Construct the line through point X
2. Construct an angle with side -rK
that is congruent to angle A.
parallel to line n.
.x
4. Draw
an oblique segment I1,I (neither horizontal nor vertical). Construct its
perpendicular bisector.
5. Draw any line m and a point l7not on m. Construct the line through
I,7'
pallallelto m.
6. Construct
an angle congruent to LXYZ.
YZ
Draw two angles like the ones shown. In Exercises 7-1O, construct
an angle with the indicated measure.
Draw three segments like the ones shown. In Exercises 11-13, construct
segments having the indicated lengths.
H
L7,.a+b
L2.
b-a
14. Copy line k and a point L not on k.
Construct the line through t that is
perpendicular to k.
c
L3.b+c
15. Copy hne m and a point R on m. Construct
the line through R that is perpendictlar to m.
P|actice BanK, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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37
DATE
NAME
1. Use inductive reasoning to find the next two numbers in
a.4,8,13,79, ? , ?
c, 0, -3, 6,-9,12, ? ,
2.
each pattern.
b.-7,4,-I,2,
? ,
?
?
Sketch an example of each figure.
a. a quadrilateral with only one pair of congruent sides
b. a hexagon with only one right angle
3. Each exterior angle of a regular n-gon has a measure of 8". Find the value of
z¿.
4. Tell rvhether a triangle having the given side lengths is acute, right, or
obtuse.
a.
16,24,32
b.24,32,40
c.42,J2,102
5. Find the length and midpoint of the segment with endpoints (9, -2)
and (-3, 6).
6. Find
the values of x, y, and z.
7. Find mLI andmL2.
2
(2x + 6)"
Use the method of proof indicated. First copy the diagram and mark
given information.
9.Key
Given: BCDE is
a parallelogr¿ìm.
Prove: LABF = LD
38
it with the
steps of a plooT
Given: L llm,
Prove: 7ll k
LI\ =
L4
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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NAME
DATE
FOR USE WITH SECTION 6.1
Can a triangle be formed from the given lengths?
L.
12 ft, 16 ft,20
4.
11
m, l2m,13 m
7.
2l
cm,40 cm, 20
LO.
ft
2.
cm
6x,8x, l0x
8
3.2in.,5 in.,9
in., 16 in.,24 n.
5. 2 cm,'7 cm, 4 cm
6.
51
8. 24 ft, 14 ft,4 ft
9.
66 cm,
lßL.
2x,3x,4x
in.
m,61 m,71 m
2l
cm,45 cm
L2. 9x,3x,5x
The lenglhs of two sides of a triangle are g¡ven.
What do you know about the third side?
L3. 6 ft,7ft
L4, 4.5 cm, 5.4 cm
15. 6 in., 6 in.
L6. 5 m,2 m
L7. 6ft,3 ft
18. 8 cm, 17 cm
L9.I4.5 m,7.2m
2O.
22.In triangle ABC, mLC
)
x,x-3
21,. 5.5
mLB 2 mLA.
m,
6.25 m
C
What do you know about the length
of
segmentÁC?
A
What do you know about the leng¡th AR?
23. mLB
> 90'
24. mLC
)
25, mLA
mLA
1 mLC
B
I
ç-*
l
mLB andmLB
_t
l
Le
mLA
Gan the three points be the vertices of a triangle? lf not, explain why not.
fi
:
mLC
1 mLB
C
---\o
26. mLC
and
^::')ïï;,Å",,1)l u',',
:::,;iå:
^ì:
îi;':
-
\¡
28. mLB > mLA
*
i,:::',,3
33. a. Try to draw a quadrilateral with sides of lengths 5 cm, 3 cm, 4 cm, and
15 cm. Is it possible?
b. Try to draw a quadrilateral with sides of lengths 5 cm, 3 cm, 4 cm, and
12 cm.Is it possible?
.
c. Try to draw a quadrilateral with sides of lengths 5 cm, 3 cm, 4 cm, and
10 cm. Is it possible?
Practice Bank,
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39
NAME
DATE
FOR USE WITH SECTION 6.2
Are the polygons congruent? lf so, name the congruent polygons.
2.J
1,.
G
4-6,
For Exercises
AMPS
=
LWBC. Complete each statement.
BC= ?
5.mLS= ?
6. PM= ?
4.
For Exercises
slv
7-9,
AWUN
= '\TRE.
7. Find the value of x.
8. Find the value of y.
9. Find the value of z.
For Exercises 1(Þ11, name all the triangles that appear to be congruent.
LL- u
Lo- n
Given:
WUIIYZL-WY:YZ, Mt
other. *Fr-a
WZ and,l4,bisect each
Prove: LWXV= AZXY
Statement.s
l. YW ll YZL_WV :
Reasons
YZ,
I/I bisect each other.
2. LWXV= LZXY
3.WX=ZX
WZ and
4.W=
?
5. LW= LZ
6. LV= ?
7. AWXV= LZXY
40
1.?
2.?
3.?
4.?
5.?
6.?
7.?
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NAME
DATE
FOR USE WITH SECTION 6.3
1. a. Which angle is included between AB
and BC?
b.In ACDE, which two sides include LECD?
Tell whether you can prove that the tdangles are congruent, lf you can, name
the congruent triangles and tell which postulate you can use.
3.24.
2.
L
11. Complete the proof.
Given: WXYZ is a parallelogram.
Prove: LXYZ =
AZWX
w
Statements
l.
WXYZ is a parallelogram.
2.ZW:XY:WX=YZ
3.XZ=XZ
4.?
Reasons
1.?
',)
3.?
4.?
12. Give the justifications for each step in the flow proof.
Given:
midpoint of XZ, XV = ZW; XV
Prove: LXW = LZWY
Y is the
Practice Bank,
ll
ZW
x
GEOMETRY: EXPLORATIONS AND APPLICATIONS
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ryL
DATE
NAME
FOR USE WITH SECTION 6.4
1. a. Which
side is included between
LD
and
LE?
b. In AABC, which angles include BC?
Tell which method(s) can be used to prove the triangles congruent. lf no
method can be used, write none.
3.
7.
For each exercise, name a pair of overlapping triangles. Tell which method can
be used to prove that the triangles are congruent.
with venex P.
LPRU: LPTQ
12. Given: LD = LC
AB LBC
DA LAB
13. Given: LWZY = LZWX
LWZX = LZWY
14. Using the drawing and the given information in Exercise 12, wite a flow
proof to show that LABD = LBAC.
15. Using the drawing and the given information in Exercise l3,write a
two-column proof to show that AWYZ = LZXW.
16. Write aparagraphproof to show that AABC
that AC ll DF, AB ll DE, and CB = FE.
42
= LDEF
given
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NAME
DATE
FOR USE WITH SEGTION 6.5
Tell which pair or pairs of triangles must be congruent in order for you to use
the definition of congruent triangles to prove each statement.
1..
DG = EG
2.
LH= LF
3. LXWV = LZW
4.ZY=XW
5. LXW = LZW
6.WZ=YX
7. LQRP
=
8.QT=ST
9.
PQ:
LSRP
PS
10. Write a flow proof.
L1..
Given: AB llDE,AC = DC
Prove: BC = EC
fn each diagram,
I
Write a two-column proof.
Given: ¡P is the perpendicular bisector of AC.
Prove: LABD= LCBD
is the perpendicular bisector
o1 AB.
12. Find the value of x.
13. Find the value of y.
14. Construct the bisector of LPQR.
15. Using angle bisectors, construct an angle
that is
1
¿ the size of LWXY.
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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43
DATE
NAME
I
FOR USE WITH SECTION 6.6
Complete.
L.
AB=
2.
2
Find the value of
mLA=
?
x. Then find each indicated lenglh or angle measure.
4. NP
N
5.AB
3x+24
8. mLT, mLS
7. mLJ
)
I
Find the value of n andthe length of AB.
10. Find the value of y and mLD.
(3y + 13)'
ln Exercises LL-L3, draw the line of symmetry for each figure. Then tell what
types of figures are formed by drawing the line of symmetry. Be as specific as
possible,
L7.,
13.
L2.
14. Write a paragraph proof to prove that 1f LABC is isosceles
with vertex C and D is the midpoint of AB,then LA = LB.
44
Practlce Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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NAME
DATE
FOR USE WITH SECTION 6.7
Find each length or measure.
t.ln
2.In
AJKL, JK = JL, and¿Z ir Uotlt
a median and an angle bisector.
a.
LPQR, PQ
PS and
nLKMJ
^lI
PR, and
are medians.
=
A. QT
b. KL
b. QR
c. mLK
d. KJ
e. wLKJM
Í. LI
t. wLKJL
3.
Complete the proof.
Given: LABC is isosceles with vertex at C.
CD is the median ø,q,n.
Prove: CD bisects LACB.
,)
Statements
Reasons
I. LABC is isosceles with
1.?
vertex at C.
CD is the median to AB.
2.
AC:
2.?
BC
a'l
3.AD=BD
4. CD = Cf)
5. AACD = ABCD
6. LACD:- LBCD
7, aõ bisects LACB.
,|
<?
6.?
7.?
For each èegment, find an equation of the line that contains the segment.
4.
the median from P
to ON
5. the altitude from P to NM
v
I
Po
4
t/
2
o
t
6. the median from P to KN
v
,
N
4
K
4
x
o
..4
a
)
Practice Bank, GEOMETRY: EXPLORATIONS AND AppLtCATtONS
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NAME
DATE
Show that each quadrilateral is a parallelogram. Then find each length or
measure.
7-.
a.
W
2. a. QR
O
b. YZ
b. wLPRS
c. WX
c. wLRSQ
3. a. AC
4. a. nLGHJ
b. DE
b. GJ
c. DB
c. wLJHK
29
5. a. nLDAB
c.DC
b.
22
48"
D
R
6. a. EJ
4
b. BC
37"
HF
c. HG
C
Sketch each quadrilateral. Mark the g¡ven ¡nformation. Tell what kind of
quadrilateral the figure is. lf the figure is a parallelogram, teil why.
= LC and LB = LD e. EFGH with EF = EH, pC = GH, and eU + fC
I LI+,I and JK =-fpt LO. NOPQ with LN = LO = LP : Le
7. ABCD with LA
g. JKLM with.fK
1J,. RSTU with diagonals RZ and
intersec,ting at
V-,
US
-RV = -TU *UU
N(-I,
L5. P(3,7), Q(7,7), R(6, 1), S(2, 1)
and WZ
=-,fll-
-Show that the points are the vertices
L3. K(2, I0), L(7, 9), M(4, 6),
L2. WXYZ with WX = YZ
= XY
of a parallelogram.
7)
L4. F(-3,0), G(0, r), H(-1,
4), I(4,
_5)
16. A(5, 8), B(8, 4), C(5,0), D(2,4)
17. Use the diagram at the right.
a. Find the coordinates of point P given that OP = a.
b. Find the coordinates of point N so that OP
= MN
and OP ll MN.
c. V/hat kind of figure is OMNP? How do you know?
18. V/rite an indirect proof to show that a parallelogram cannot have
four acute angles.
48
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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NAME
DATE
FOR USE WITH SECTION 7.3
Classify each quadrllateral. Be as specific as possible.
1. ñ-----7t
2.
6.
6.5
12
Use the axes of a coordinate plane as the diagonals of a quadrilateral. Sketch
each quadrilateral with its given conditions. Give appropriate coordinates for
the vertices of each quadrilateral.
7. a kite whose vertical diagonal is
8. a kite whose horizontal diagonal is
longer than its horizontal diagonal
9.
a square with area 2 square units
longer than its vertical diagonal
LO. atrapezoid
11. a rhombus whose horizontal diagonal 12. a rhombus whose vertical diagonal is
is shorter than its vertical diagonal
shorter than its horizontal diagonal
13. Give the reasons for this two-column proof showing that the
diagonals of a parallelogram bisect each other.
Given: ABCD is a parallelogram.
Prove: AC andBD bisect each other.
Statements
l.
ABCD is a parallelogram.
2. AD llBC andAB ll CD
3. LBDC = LDBA and
LCBD = LADB
4.BD=BD
5. AABD = ACDB
6.AB=CD
7. LAEB = LCED
8. AAEB = ACED
9. EA:lC, aE = DE
10.
AC
and
BD bisect each other.
Reasons
1.?
t,)
3.?
4.?
{?
6.?
7. ?
8.?
9.?
10.
?
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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49
NAME
DATE
FOR USE WITH SECTION 7.4
For Exercises L-L7, find the area of each polygon.
L.
l._24_________-1
2.
3.
11
5
6.
l+_
7.
g
t2
_____Ðl
10
12
12.
5\/,
13. a square with side length 34 cm
L4. a nght triangle with a leg of length 12 in. and a hypotenuse of length 20 in.
15. a rectangle with sides 14 mm and 9 mm
16. an isosceles triangle with base 10 in. and perimeter 36 in.
17. a square with perimeter 48 m
The coordinates of the vertices of a polygon afe g¡ven. Find the alea of
the polygon.
L8. W(-2, -I), X(-2,3), Y(2,3), Z(2,
-7)
20. A(4,3), B(4,6), C(3,6), D(3,3)
22. M(4, 1), N(1, 7), P(4, 4), Qel, 4)
50
L9. p(-2,2), Q(0,2), R(4, -2), 5(-6, -2)
27..
E(-3, -r), F(-r,6), G(5, -1)
23. J(1, 4), K(5,2), L(I,
4), M(-3, 2)
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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NAME
DATE
FOR USE WITH SECTION 7.5
Find the area of each shaded region. Each polygon is regular.
Find the area of each shaded region. Each outer polygon is regular.
13.
8
')
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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51
DATE
NAME
I
FOR USE WITH SECTION 7.6
Flnd the volume and surface area of each prism or cylinder. In Exetclses 1-3,
the bases for the prisms are regular polygons.
6.
Ð.
8
C=44
15
Each net folds into either a prism or a cylinder. Find the volume and surface
area of each prism or cylinder.
Find the volume of each object described.
13. Each edge of a cube is 4 in. long.
L4. Atriangular prisrh is 12 in. long. The perimeter of the
area of the base is 12 in.z.
base is 24 in. andthe
The vertices of a prism are g¡ven. Sketch the prism and find its volume.
15. A(0, 0,4), B(0,4,4), C(3,0, 4), D(0,0, 0), E(0, 4, 0), F(3, 0, 0)
16. p(0, 0, 4), Q(0, -3, -4), R(l 1, -3, 4),S(1 1, 0, 4), T(0, 0, 1), U(0, -3, l),
y(ll, 0, 1), w(11, -3, 1)
52
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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NAME
DATE
a
CUMUTATIVE PRACTICE THROUGH CHAPTER
1.
7
The midpoint of AB is C, the midpoint of AD is B, and BC =' 5.1 . Find AD.
3. Find
the value of x,
ACB
D
mLA, andwLCBF.
(5x
B
-20)"
Find each indicated lengith or angle measure.
4. Kite
a.
ABCD
5. Rhombus PQRS
B
AD
P
a.,SR
A
C
b. DC
b.s0
s
8. ParallelogramPQRS
7. ParallelogramWVXY
a.W
b. YZ
c. WX
43
v
.1
9. Rectangle ABCD
Q
A
a.BD
A.QR
b. nLPSR
b. BC
c. nLSRQ
c.CD
D
Find the area of each polygon, circle or shaded feg¡on.
L4.
F---gr
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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53
DATE
NAME
FOR USE WITH SEGTION 8.1
ln the diagram,
A'ggùE
is the image
1. What is the image of AB? of
2. Name
a triangle congruent
o1
ABCDE after a reflection over line
k
CA?
to LDEC.
3. Name a triangle congruent to ADEA.
4. Name
a figure congruent to
B'C'D'E'.
5. Name two angles in the diagram that have the
same measure.
6. What is the image of A'B'C'D'E' after a reflection
over line k?
Gopy each diagram. Sketch the image of the polygon after a reflection over the
g¡ven l¡ne. Labelthe image polygon.
7.
8.
9.
)
c--'\
Each diagram shows a polygon and its image after a reflection. Gopy each
diagram and draw the line of reflection.
Each diagram shows a polygon and its image after a reflection. Give the
missing measurements.
L4.
L3.
16. Draw three different types of polygons. Reflect each over the same line of
reflection. Label the vertices of the polygons and their images. Write
statements about the congruence of the figures.
54
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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DATE
Reflect each polygon over the yaxis. Find the coordinates of the vertices
of the image.
2.
Reflect each polygon over the x-axis. Find the coordinates of the vertices
of the image.
6.
x
Reflect each polygon over the line y = x. Find the coordinates of the vertices
of the image.
9
10. Use the polygon for Exercise 7 and its image. Find the coordinates of the
midpoint of each segment that joins a vertex to its image. Do all of these
midpoints lie on the line y =,x? How do you know?
11. Use the polygon for Exercise 8 and its image. Find the coordinates of the
midpoint of each segment that joins a vertex to its image. Do all of these
midpoints lie on the line y = x? How do you know?
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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55
DATE
NAME
FOR USE WITH SECTION 8.3
Gopy quadrilateral ABCD and draw its image after each translation.
L. (x,y) +(-x+3,y+2)
2. (x,y) -+ (¡- 4,y +2)
3. (x,y)-+(x-3,y-3)
4. (x, y) -+ (x, y + 2)
5. (x, y) -+
6.
(-r
+ 3, y)
(x,y)-+(x-2,y-3)
Describe each translation using coordinate notation.
7. Every point moves to the left
(
x
3 units and down 2 units.
8. Every point moves to the right 4 units.
L
D
9. Every point moves down 5 units.
10. Every point moves to the left 1 unit and up 8 units.
The image of each polygon after a translation is shown below Describe
each translation using words followed by coordinate notation.
Lt.
L2.
lãtl@
so that
toï-ranslatê the pattern
it matches itself.
15.
16.
t)
56
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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NAME
DATE
FOR USE WITH SECTION 8.4
Name the image for each rotation around the or¡E¡n. The coordinates of the
vertices are inteters.
1.
Rotate ABCD90".
2. Rotaie EFGH
3.
Rorate JKLM 270".
4. Rotate WXYZ360".
180".
5. Find the coordinates of each image.
a. EFGH
c. WXYZ
b. JKLM
Copy each diagram and draw the image of the polygon after a rotation with the
given measure and center P,
6. rotate
120o
7.
Sketch the image of each polygon after a 9O' rotation around the oritin.
9.m
10.
L1,.
v
6
c
v
x
x
Sketch the image of each polygon after a 180' rotation around the orlfl¡n.
L2.
13.
v
v
.i
C
Practice Bank,
x
c
x
GEOMETRY: EXPLORATIONS AND APPLICATIONS
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57
DATE
NAME
FOR USE WITH SECTION 8.5
Plot the triangle whose vertices are g¡ven. Then find the image of the triangle
after a glide leflection using the given translation and reflection.
t . A(3, 2), B(-I, -2), C (0, 4)
translation: (x,y) -+ (x-3,y)
reflection: over the x-axis
2. A(6, 0), B(2, 0), C(4, 4)
translation: (x, y) -+ (x, y + 3)
reflection: over the y-axis
x
C
4. A(4,2), B(2,4), C(3,I)
translation: (.x, y) -+ (x + 2, y)
reflection: over the .r-axis
3. A(2,0), B(0, 2), C(3,3)
franslation: (x, y) -+ (x, y - 4)
reflection: over the y-axis
v
x
C
5. J(2,2), K(-1,1), L(0,3)
translation: (x, y) -+ (x + I, y +
reflection: over the line y = ¡
6. y(-3, -l), w(I,2), x(3, r)
1)
translation: (x, y) -> (x + 2, y - 2)
reflection: over the line y = -y
v
À
(
(
58
x
x
Practlce Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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NAME
DATE
FOR USE WITH SEGTION 8.6
1. Draw the image of AAOC after the dilation with the
v
given center and scale factor.
a. center C andscalefactor2
b. center
2.
andscale factor 1
O
2
In AABC,let P and Qbe the midpoints of AC and BC, respectively. Find the
center and scale factor of the dilation that moves LABC to LPQC.
3. In ARBZ, letA be the midpoint of BR and let C be the midpoint of BZ. Find
the center and scale factor of the dilation that moves AABC to ARBZ.
Draw the image of each figure after the dilation with center O and the given
scale factor.
4.
scale
)
factor:
5.
J
7. scale factor 2
8.
scale factor
I
2
^1 2
scale Iactor
v
9,
scale factor
A
l
3
to
scale factor 3
v
,a
6.
)
x
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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DATE
CUMUTATIVE PRACTICE TI{ROUGH CHAPTER
1. Name
8
the measure of a complementary angle, a supplementary angle and
vertical angle for 75'.
2. Find
the lengths of the sides and identify the type of triangle
if
the vertices
arcA(2,3), B(3, -1); and C(5, -1).
3. The lengths of two sides of a triangle arc 17 and32. What do you know
about the third side?
Gepy cach dlagram. Sketch the image of the polygon after a reflection over the
glvcn llne. Label the image polygon.
6.
4.
Draw and label each polygon. Then reflect the polygon over the line y =
label the vertlces and find thelr coordinates.
¡.
7. Triangle ABO with vertices A(-1,2), B(1,3), and O(0, 0)
8. Trapezoid HJKL with vertices H(4,2), J(-1,5), K(1, 4),
9.
and
L(-5, -Z)
Sketch the polygon in Exercise 8 after a 90o rotation, a 180" rotation, and a
270" rotation around the origin.
Descllbe each translation using coordinate notation.
10. Every point moves to the right 12 units and down 7 units.
11. Every point moves to the left 3 units and up 9 units.
Sketch thc lmage of the triangle with the g¡ven vert¡ces after a gl¡de reflection
uslng the g¡yen translation and reflection.
7.í2.
A(4,2), B(3, -1), C(5, 0)
translation: (x, y) -+ (x + 3, y)
reflection: over the .r-axis
L3. D(I,4), E(3, -l), F(4, 5)
translation: (x, y) -+ (¡, y - 5)
reflection: over the y-axis
1¡1. Draw a triangle on a coordinate plane. Show the image
of the triangle after a
with a scale
dilation with center at the origin and a scale factor of 3. Repeat
factor of
60
1.
3
Practice Bank, GEOMETRY; EXPLORATIONS AND APPLICATIONS
Copyright @ McDougal Littell lnc. All rights reserved.
NAME
DATE
FOR USE WITH SECTION 9.1
Solve each proportion.
3x
2.
1_2s
7y
3.
5t
t45
4.7:15=m:20
5.
6:k=k:24
6.
r:9=56:72
2r. -5_57
9x--
8.
6.8
v
9. 5 : 6 =7
¿.
--824
8.1
3.4
:z
Tell ì/yhether each pa¡r of shapes is similar.
10.
7l-.
L2.
4
8
13.
Find-the-indicated angle measure or length-for each pair of-simflar llgUres.
16.
L7.
18.
JJ
')
19. A graphic artist has designed a logo for a business. The logo on the graphic
designer's original drawing is 5 in. high and 6.5 in. long. The business
owner wishes to have the logo painted onto the side of a delivery truck. If
there is enough room to.enlarge the logo to a height of 24 tn., how long will
the enlarged logo be?
Practice Bank, GEOMETRY: EXPLORATIONS AND
APPLTCATIONS
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DATE
NAME
FOR USE WITH SECTION 9.2
ls it possible to prove that the triangles in each pair are similar? Explain why or why not.
7.
3.
2.
L.
LABC
-
LDEF, mLB = 70", mLC =
35o, AB
= 12, and DE = 4.
a. Sketch the two triangles.
b. Find the measure of each angle in the triangles.
c. What is the value of the ratio
8.
4?
AC
LJKL- LPQR,nLJ=57",mLK
= 90o, JL=5, andPR =17.5.
a. Sketch the two triangles.
b. Find the measure of each angle in the triangles.
9. Write a two-column proof.
Given:
IJ INK, LN = LK
Prove:
# =X
J
1O. Write a flow proof.
Y
Given: XYIIWZ
l|rove:
62
WV
VZ
vxw
Practlce Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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DATE
Find each indicated length.
3.
For Exercises 4-9, complete the equation so
.-x5propoltlon
4.1-
=
it is equivalent to the
-.
5.
?
B.
q=
6,**j =
?
v
"n5=
v+6
9.
?
?
I =?
5
For Exercises 10 and 11, use the diagram at the dght. ,48 = 4, CA = 6, and
CB = 7. The diagram is not drawn to scale.
LO.If D is the midpoint of AC
lengths CD, CE, aîdDE.
L1,.If D is
and E is the
midpoint of CB, find the
I
of the way from C to A, and E is
4'4
I
of the way from
C to B, find the lengths CD, CE, aîd DE.
For Exercises 12 and 13, use the diagram at the right. .ABCD is a
paralfefogram, AB = tO, AD = 6, and DB = L2. The diaEram is not drawn
to scale.
L2.If
E is the midpoint of DA and G is the midpoint of BC, find the
lengths CG, DF, EG, and FG.
13. lf E is ] of the way from A to Ð and G is I of the way from
3'3'
C
E
A
F
B
B to C, find the lengths AE, CG, EF, FG, DF, and FB.
In the proportion
: = *,
6 is the geometric mean of 2 and 18. Solve each
proportion to find a geometr¡c mean. Give only the positive solut¡on.
L4.1=
!-
x2O
15.
q=¿
.r
18
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x =L
252
L6.7
63
DATE
NAME
ln Exercises 1-3, APQR
-
LJKL.
1. Find the value of the ratio 4.
KL
2. Find the ratio of the areas.
RJ
t2
3. Find the ratio of the perimeters.
10.5
For Exercises 4 and 5, use the similar prisms at the r¡ght.
4. Find the surface
arca of B.
5. Find the volume of A.
A
S.A. = 608
l6
Each palr of figures is similar. Find each missing value.
8.
3'2
P=9.6 P=
A_?A=?
?
r= ?
C- ?
r=
?
B 7m C D
Ratio of oerimeters
F
=
?
LPQR and AB i PQ - 4 : 7 .Whaf is the ratio of their
perimeters? What is the ratio of their areas?
9. a. LABC
-
the shortest side. What is the corresponding altitude
in
APQR?
For Exercises 10-12, answef the questions about each situation. lt may help
to sketch each figure.
1O. The lengths of the sides of a polygon are tripled. How does this change the
lengths of the diagonals? the perimeter of the polygon? the area of the
polygon?
11. If two cubes have volumes in the ratio of 64 : 27 , what is the ratio of the
lengths oftheir corresponding sides? oftheir surface areas?
L2. The sides of a triangle measure 10 cm, 24 cm, and 26 cm, respectively.
How long are the sides of a similar triangle whose. area is 480 cm2?
')
64
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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NAME
DATE
For Exercises 1-6, find the probabirity of hitting
the shaded area of the target
with a randomty thrown dart that hlts the target.
2.
12
7.
segments are all congruent. What is the
ected at random on the segment is closer to
8' on xZ, whatis
the probability of a randomly selected point being
within 4 cm of point y?
a.
ln A,q!C, _-?l ll 1'n, lC = 4CO,
ana
to the area of AABC?
10 cm
8cm
Z
x
C^ = ¿cn._\Àlbat_is+he_ratie_ef+he__
b' rf aABC is a darl board, what is the probability of a randomry
thrown
dart landing in ABED?
what is the probabirity of hitting the shaded area of the
target with a randomry
thrown dart that hits the target?
r\
7\
\.)
¡.y'
H rf
Practice Bank, GEoMETRy:
EXpLoRATTONS AND AppLrcATroNS
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I
65
DATE
NAME
CUMULATIVE PRACTICE THROUGH CHAPT.ËR 9
1,.
Find the area of an isosceles triangle with base 17 cm and perimeter 37 cm.
2. Show that the points A(-10, 2),
of
3.
B(4,
16), C(6,6), and D(0,
-8)
are vertices
a parallelogram.
Sketch three lines
j,
k, andru such
thati ll k and lines j andm are skew.
4. Solve each proportion,
-8 20
^.1=!5. Is
b.2={
4 y
c. 8: k =k:!28
it possible to prove that the triangles in each pair are similar? Explain why
or why not.
6. Find each indicated length.
b.
3sy'-7----.-+o
'. ')
-----\
l6
7.
TWo regular octagons have sides of lengths 9 cm and 13 cm'
a.
'What
is the ratio of the lengths of their corresponding sides?
b. What is the ratio of the lengths of their diagonals?
c. What is the ratio of their perimeters?
d. What is the ratio of their areas?
8. Find the geometric probability of hitting the shaded
area of the target
with
a
randomly thrown dart that hits the target.
b.
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
Copyright @ McDougal Littell lnc' All rights reserved.
\r
NAME
DATE
FOR USE WITH SECIION 1O.1
G7,
For Exercises
7,.
use the diagram to complete each statement.
LXYZ=?
2. LWXZ
4. WZ is the geometric
mean
-
of ? and
5. XZ is the geometric mean of ? and
^wx
WZ WY
?
?
?
?
6. ZY is the geometric mean of ? and ?
.
.
.
7.If WX=4andXY=9,fhenXZ= ?,WZ= S,andYZ=
?.
ldentify the similar triangles.
8.¿
DC
9.
B
Find the geometric mean of the given numbers.
10. 2 and
L1,. 0.25 and 400
18
L2. 15 and20
Find the value of each variable.
2'1
16.
18.
19. Write a two-column proof.
Given: AXYZhasnght LZ.
ZW is the altitude to XY.
Provez! =L
hb
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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DATE
NAME
FOR USE WITH SEGTION LO.2
Find the missing side lengths of each triangle.
9.
I
600
q
t2'
,t r
/'----------t>-
.rt
-4
l*
6{3
16. Construct a 30-60-90 triangle.
17. Construcf a 4545-90 triangle.
68
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
Copyright O McDougal Littell lnc. All rights reserved.
NAME
DATE
FOR USE WITH SECTION 1O.3
ln Exercises L4, Íind tan A and tan 4 then find the measures ol
Round angle measures to the nearest tenth of a degree.
L.
LA
and
LB.
2.c
B
9
5
B
C
3.
4.
Find the value of each expression. Round youf answers to four decimal places.
5. tan 50"
9. a. Use the triangles
6. tan 14"
7. tan 3.8"
shown. Find the missing side lengths.
b. Find the values of tan 30o, tan 45", and tan 60o. Write your answers
in radical form.
Find the measure of the acute angle that satisfies the given equation. Round
your answers to the nearest tenth of a degree.
LO. tan A
=?
9
L1,. tanB
=E
,7
L2.tanC=3.123
13. tan C=0.9714
3l
L7. Atree on level ground
casts a shadow 30 feet long. The angle of elevation
from the tþ of the shadow to the top of the tree is 70". Find the height of
the tree.
18. From the top of a 575-ft high bluff, a rescue scout looks down upon a hot-air
balloon accident. The angle of depression is 7". How far is the accident from
the rescue team at the foot of the bluff?
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATTONS
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DATE
NAME
FOR USE WITH SEGTION 1O.4
ln Exercises 1-3, find sin A, cos A, sin B and cos B,
3.
Find the value of each expression. Round your answers to four decimal places.
4. sin 62o
5. sin 4.9'
6. cos 88o
7. cos 43.8o
Find the measure of an acute angle that satisfies the given equation. Round
your answels to the nearest tenth of a degree.
g.
rinX=l
9. sin P =0.1239
10.
cos
H=0.7064
11. cos N=
l;
Find the value of each variable. Round your answers to the nearest tenth.
L2.
13.
Find the measure of each acute angle. Round your answers to the nearest
tenth of a degree.
15.
L7.
16.
B
5
C
2.,11
Use the triangles at the right
to find the exact value of each expression.
18. sin
45'
19. cos
45"
21. sin
60'
22. sin 30'
2O. cos 60o
23. cos 30o
24. To be used safely, a ladder should make an angle of about 75" with
the ground.
a. How far should the foot of a20-ft ladder be from the base of
a
building?
b. How long should a ladder be in order to reach a window that is 36 feet
above the ground? How far should its foot be from the base of the
building?
70
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
Copyright @ McDougal Littell lnc. All rights reserved.
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DATE
FOR USE WtrH SECTTON 10.5
Express each vector in component form and find the value of each variable.
L.
2.
C
3.
wo
?o
F
E
Graph each vector and find ¡ts magn¡tude,
nj
= (9,2)
S.
KL= (_5,7)
L AT= (3, 0)
g.
CO =
4.
(4,4)
6. MN = (6, _6)
10.
¿fi= ç2,5)
7. PQ =
Ç5,3)
L1.. G-H=
(4, -3)
L2. Graph each scalar multiple of RS and find
its magnitude.
a. 2RT
¡.
lnJ
2
c. -3RT
d. lR.s
3
AB = (-L,21, TD = (-6, 41, and EF = (3, -1). Use a graph to find each
vector sum, and write the resulting vector in component form.
T3.
AB+ CD
rc.2¿,n +
Lg.
lo
L4. AB + EF
15.
CD+EF
L7. AÈ+zcõ
18.
zîo+
E^r
EF.= Q, Ð and GE = (-3, 2). Use the parallelogram method to find
EF +GH.
The magnitude and direction of a vector are labeled on each diagram. Use
trigonometric ratios to find each unknown lenglth. Then express the vector in
component form.
21,.
22.
a
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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7L
DATE
FOR USE WITH SECTION 10.6
Find the area of each polygon. Round your answers to the nearest hundredth.
18
35"
13. The length of each side of a regular octagon is 10. Find the area
of the octagon.
of-+-regular pentagon is 14Æin4the area
of the pentagon.
15. Find the area of a regular hexagon with side length 8.
16. Find the area of a regular octagon with apothem 6.
Find the volume of each prism. Round your answerc to the nearest hundredth.
L7.
680
19.
Base:
regular
hexagon
H
72
4
Practice Bank, GEOMETRY: EXPLORATIONS AND APPLICATIONS
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NAME
DATE
IFOR USE WITH SECTION TO.7
Find the he¡ght and slant helght of each cone. Then find the radius of
each base.
Flnd the helght and slant height of each regular pyramid.
,
Find the volume and surface area of each right cone or regular pyramid.
Find the volume of each ¡egular pyramid.
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