Download Geometry Name_______________ Practice Test: Chapter 4

Geometry
Practice Test: Chapter 4
Name_______________
Directions: For problems 1-10 determine if the statements are either TRUE
or FALSE. Justify all of your answers with an example, counter example,
explanation, or conjecture. You may also change FALSE statements so that
they are true.
1. If two sides and the included angle of one triangle are congruent to
two sides and the included angle of another triangle, then the triangles
are congruent.
2. In any triangle the angle bisector of an angle is also a median of the
triangle.
3. It is possible to construct a triangle with side lengths, 29cm, 38 cm,
and 57 cm.
4. If the measure of an exterior angle of a triangle is 135o then the sum of
the two corresponding remote interior angles must be 135o also.
5. If ΔABC is isosceles and CA ≅ CB then ∠A ≅ ∠C .
6. Suppose that there are triangles, ΔABC and ΔDEF , such that
m∠A + m∠B = m∠E + m∠F , then it must be true that m∠C = m∠D .
2. The sum of the measures of the three angles of an obtuse triangle
Part A
is greater
than the sum of the measures of the three angles of an
Identify each statement as true or false.
acute triangle.
1. The letters CPCTC are an abbreviation for the phrase “corresponding
3. If the base
of an triangles
isoscelesaretriangle
each
partsangles
of congruent
congruent.
” measure 37°, then the
o
o
vertex
measures
106°.
7. For
, if msum
is the
shortest
∠
A of
= 78
m∠B =of52thethen
ΔABC
2.angle
The
theand
measures
threeAB
angles
of an
obtuseside.
triangle
is greater than the sum of the measures of the three angles of an
4. If a triangle
has two angles of equal measure, then the third angle
acute triangle.
is obtuse.
3. If the base angles of an isosceles triangle each measure 37°, then the
o
8. 5.
If If46two
is the
measure
one of106°.
the base
angles
of antriangle
isosceles
the
sides
and
non-included
angle
of one
arethen
congruent
vertex
anglea of
measures
o
measure
the vertex
angle is 98 . angle of another triangle, then the
to two of
sides
and a non-included
4. If a triangle has two angles of equal measure, then the third angle
€
trianglesis are
congruent.
obtuse.
5. If two sides
and
one lengths
triangle are
6. It is possible
to construct
a triangleangle
withofside
12 congruent
cm, 15 cm,
€ a non-included
to
two
sides
and
a
non-included
angle
of
another
triangle,
then the
and
25 cm.
9. The
letters
CPCTC are an abbreviation for the phrase “congruent
triangles
are congruent.
parallelograms
correspond
to circles.”
! is
7. For !ABC, if m"A ! 52°, m"B ! 88°, and m"C ! 40°, then AB
6. It is possible to construct a triangle with side lengths 12 cm, 15 cm,
the shortest
and 25side.
cm.
! isangle.
8. The altitude
to theif base
an isosceles
triangle
bisects
the
vertex
7. For !ABC,
m"A of
! 52°,
m"B ! 88°,
and m"C
! 40°,
then
AB
the shortest side.
If the measure of is
anaexterior
angle
of a triangle is 45°, then each of the
10.9.Angle-Angle-Angle
congruence
shortcut.
8. The altitude
to theinterior
base of an
isosceles
bisects the
vertex angle.
corresponding
remote
angles
alsotriangle
has measure
45°.
9. If the measure of an exterior angle of a triangle is 45°, then each of the
10. Side-Angle-Angle
is remote
a congruence
shortcut.
corresponding
interior angles
also has measure 45°.
10. Side-Angle-Angle is a congruence shortcut.
Part B
If possible,
use
given information
to complete
Directions:
IfPart
possible,
the congruence
statementthe
andcongruence
tell which
B thecomplete
congruence
conjecture
supports
the information
statement.
If
triangles
cannot
statement
and telluse
which
congruence
conjecture
supports
the be
congruence
If possible,
the given
to the
complete
the congruence
shown
to be statement
congruent
from
information
given,
write
“Cannotthebecongruence
tell the
which
congruence
conjecture
statement.
If the and
triangles
cannot
be shown
to
besupports
congruent
from the
statement.
If
the
triangles
cannot
be
shown
to
be
congruent
from
the
determined.”
information given, write “Cannot be determined.”
information given, write “Cannot be determined.”
! ! _____
11.1. !MXD
1. !MXD ! ! _____
D
T
D
! ! _____
12. 2. !TAM
2. !TAM ! ! _____
MM
T
3. !BNG ! !
3. !BNG ! ! ____
CC
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X
X
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26
26
CHAPTER 4
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Discovering Geometry Assessmen
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CHAPTER 4
Discovering Geometry As
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the congruence
upports the congruence
congruent from the
Chapter 4 • Test (continued)
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3. !BNG ! ! _____
! _____
4. !NMT ! ! _____
Period
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13.
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Date
Period
1. a ! _____
2. b ! _____
3. c ! _____
4. d ! _____
6.
! ! _____
5. !MPD
e ! _____
6. f ! _____
7. gD! _____
C8.
Date
T ! 4.
! !NMT
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5. !HOW ! 5.
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d angle. p " q
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d
_____
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2
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1.
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164°
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! ! BE
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Flowchart Proof
_____
q
q
R
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Show:
_____
p
p
h ! _____
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Provide
each missing reason or statement in this flowc
C
D
C
Given:
"D ! "CC
16.
E
! ! EC
!
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Part C
measure
lettered
angle.lettered
p " q angle. p " q
Find of
theeach
measure
of each
____ 1. a ! _____
2. b ! _____2. b ! _____
___ 3. c ! _____
4. d ! _____4. d ! _____
___ 5. e ! _____
6. f ! _____6. f ! _____
p
e
____ 7. g ! _____
8. h ! _____8. h ! _____
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15.
W
Part C
R angle. p " q
Find the measure of each lettered
(continued)
Y
Period
14.
P
6. !MPD ! ! _____
MT
O
6. !MPD ! ! _____
B
W
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M
Y
• Test
(continued)
Chapter
4 • Test (continued)
Name O
5. !HOW ! ! __
Date
5. !HOW ! ! _____
O
P
f
q
d
a
b g
h
164°
c
2.
a 144°
b 3.g
h
c
c
7.
! !!! ! ! !!!
8.
4.
f
5.
q in this
ch Provide
missing each
reason
or statement
flowchart proof.
missing
reason or
statement
164° in this flowchart proof.
6.
C
"D
! "C "D ! "C D
fC
D
Given:
E
! ! EC
!
E
DE
! ! EC
!
DE
1 2
1 2
Part E
! ! BE
!
AE
! Find
!the measure
B
Show:
AE
!ABE
of each
lettered Bangle. Given line p is parallel to line q.
A
Write a proof of this statement.
Proof
Flowchart Proof Show your work.
! ! PQ
!
Given:
PR
D
C
1.
! ! PS
!
PT
E
tatement in this flowchart proof.
2.
3.
4.
5.
1
2
7.
17. a = _____ 18. b = ______
19. c = ______
9.
! !!! !7.! !!!
! !!! ! ! !!!
B
9.
21.
8. e = _____ 22. f = ______
10.
8.
Show:
P
20. d = ______
S
! ! RT
!
QS
R
23. g = ______
10.
24. h = ______
Discovering Geometry Assessment Resources A
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Part E
©2003 Key Curriculum Press
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Part
3. Cc ! _____
4. d ! _____
Find the measure of each lettered angle. p " q
d
a 144°
e ! _____
6. f ! _____
e
b
p
g h
a ! _____
2. b ! _____
g ! _____
8. h ! _____
q
c ! _____
4. d ! _____
d
164°
f
25.
each missing6.reason
or statement in this flowcharta proof.
Part
De ! _____
144°
5.Provide
f ! _____
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p
Provide each missing reason or statement in this flowchart
proof. b g h
7. g ! _____
8. h ! _____
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Given:
"D ! "C
q
E
164°
! ! EC
!
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f
5.
1.
7.
3.
c
c
Part D
1 2
! ! BE
!
Show:
AE
A
B
Provide each missing reason or statement in this flowchart
proof.
Flowchart
Proof
D
C
Given:
"D ! "C
E
!
!
1.
DE ! EC
1 2
! ! BE
!
Show:
AE
2.
A
B
Flowchart
Proof
3.
1.
5.
3.
7.
9.
! !!! ! ! !!!
8.
4.
10.
2.
6.
7.
9.
! !!! ! ! !!!
4.
8.
10.
Part E
5.
26.Write
a proof
forstatement.
the following using any method.
Write a proof
of this
6.
! ! PQ
!
P
Given:
PR
!
!
PT !
PS m∠RSQ ≅ m∠QTR
Given: SQ ≅ RT
and
S
T
Part
E
Prove:
SR
≅
TQ
!
!
Show:
QS ! RT
Write a proof of this statement.R
Q
! ! PQ
!
P
€PR
€ Given:
!
!
PT ! PS
S
T
€
!
!
Show:
QS ! RT
Discovering Geometry Assessment Resources A R
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CHAPTER 4
27
©2003 Key Curriculum Press
Discovering Geometry Assessment Resources A
©2003 Key Curriculum Press
CHAPTER 4
27