Download Midterm Review

Midterm Review
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Date:
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Draw pictures and show work as appropriate.
1.
3.
Which shape, if rotated 90 , will coincide with
itself? (“Coincide” means means there's an
exact match between the set of points, or one
shape will lay perfectly on top of the other.)
A.
rectangle
B.
equilateral triangle
C.
parallelogram
D.
square
Look at this gure:
If the gure is rotated a certain number of
degrees, the transformed gure will coincide
with (overlap) the original. Which of these
cannot be the rotation?
A.
C.
2.
240
180
B.
120
D.
320
What is the the rotational symmetry of a
rhombus?
4.
A.
120
B.
100
C.
90
D.
60
Which of the following letters does not exhibit
line symmetry?
A.
page 1
X
B.
Y
C.
W
D.
Z
5.
Given a ^ABC in a coordinate plane and its
image gure ^A0 B 0 C 0 after any translation,
which of the following are always true?
I.
8.
The distance AA0 and BB 0 are equal.
AA0
and
III. The distances
equal.
BC 0
II. The lines
BB 0
and
are parallel.
B0C
are
IV. mOA = mOA0
6.
A.
I only
B.
IV only
C.
I and II only
D.
I, II and IV
In the gure, mOCNA = mOWAN and
CN = WA. What congruence statement proves
^CAN = ^WNA ?
A.
SAS
B.
ASA
C.
SSA
D.
not necessarily congruent
^DEF is labeled in a clockwise direction.
After a sequence of translations, R is the
translation of ^ DEF .
a) After 3 translations, what is the
orientation of R?
9.
b) When is the orientation of R not the
same as ^DEF ?
7.
State the congruence relation for ^FLE and
^FUE.
A.
ASA
B.
AAA
C.
SSA
D.
SSS
page 2
In the diagram, AC = AD and AB bisects OA.
Which congruence method is therefore used
to conclude that ^ABC = ^ADB ?
A.
ASA
B.
SSA
C.
SAS
D.
AAA
Midterm Review
10.
If the triangles can be proved congruent using
only the information marked on the diagram,
what is the reason?
A.
SSA
B.
ASA
C.
SAS
D.
cannot be proven congruent
11.
page 3
In the gure, XYWZ is an isosceles trapezoid.
Which pair of triangles can be proved to be
congruent with the result that OXWZ = OYZW
by CPCTC?
A.
^ZPW and ^YPX
B.
^XZY and ^YWX
C.
^XZW and ^YWZ
D.
^XZP and ^YWP
Midterm Review
12.
Which diagrams show two triangles which must be congruent?
I.
A.
13.
II.
II only
B.
III.
I and II only
C.
If the vertical brace is a line segment of
symmetry for the kite, how many pairs
of congruent triangles are formed by the
2 braces?
A.
5 pairs
B.
3 pairs
C.
2 pairs
D.
1 pair
14.
page 4
I and III only
D.
II and III only
The SAS congruency axiom states that two
triangles are congruent if:
A.
two angles and the contained side of one
triangle are equal to two angles and the
contained angle of the other triangle.
B.
two sides and the contained angle of one
triangle are equal to two sides and the
contained angle of the other triangle.
C.
two angles and a side of one triangle are
equal to two angles and a side of the
other triangle.
D.
two sides and the excluded angle of one
triangle are equal to two sides and the
excluded angle of the other triangle.
Midterm Review
15.
Which congruency theorem is described
below?
17.
“In two triangles, if three pairs of sides
are equal in length, then the triangles are
congruent.”
A.
16.
SSS
B.
SAS
C.
ASA
D.
In the diagram, lines a, b, and c are parallel,
with the two remaining lines intersecting line b
at the same point. x, y, and z are measures
of angles. To show that y z = x, which
of these angle de nitions or relationships is
necessary?
AAA
A.
right angles
B.
acute angles
C.
obtuse angles
D.
vertical angles
By the ASA congruency axiom, two triangles
are congruent when 2 angles and the
contained side of one triangle equal
of the other triangle.
A.
at least 2 angles
B.
any 2 angles and any side
C.
2 angles and the contained side
D.
3 sides
page 5
Midterm Review
18.
Given:
O1 and O2 are supplementary
Prove:
mkn
Statement
Reason
1. O1 and O2 are suppl.
Given
2. mO1 + mO2 = 180
def'n of suppl. angles
3. mO3 + mO2 = 180
def'n of straight angles
4. mO1
subtr. property of equality
mO3 = 0
5. mO1 = mO3
add. property of equality
6. m k n
In the proof, what is the reason for statement 6?
A.
If two lines are cut by a transversal, and the alternate interior angles are congruent, then the lines
are parallel.
B.
If two lines are cut by a transversal, and the same-side interior angles are congruent, then the lines
are parallel.
C.
If two lines are cut by a transversal, and the alternate exterior angles are congruent, then the lines
are parallel.
D.
If two lines are cut by a transversal, and the corresponding angles are congruent, then the lines are
parallel.
page 6
Midterm Review
19.
Given:
AD = DC
mOBAC = mOBCA
Prove:
BD bisects OABC
statement
reason
mOBAC = mO BCA
(1)
AB = BC
(2)
AD = DC
(3)
BD = BD
(4)
^ABD = ^CBD
mO1 = mO 2
(5)
(6)
In the above proof, what is reason (2)?
A.
given
B.
sides opposite equal angles are equal
C.
isosceles ^
D.
CPCTC
page 7
Midterm Review
20.
Using the given diagram, Rochelle writes a proof to show that if OSEM = OILM, then ^MEL is isosceles.
Statement
Reason
1. OSEM = OILM
2. OSEM and OMEL are a linear pair
OILM and OMLE are a linear pair
1. Given
2. De nition of Linear Pair
3. OSEM and OMEL are supplementary
OILM and OMLE are supplementary
3. Linear Pair Postulate
4. OMEL = OMLE
4.
5. ME = EL
5. If two angles of a triangle are =,
then the sides opposite them are =
6. ^ MEL is isosceles.
6. De nition of Isosceles Triangle
What reason should Rochelle use to justify the fourth step?
A.
Supplementary angles are congruent.
B.
Linear pair angles are congruent.
C.
Angles that are supplements of congruent angles must be congruent.
D.
Exterior angles are congruent.
page 8
Midterm Review
21.
22.
Quadrilateral PARK is a parallelogram with
OPAK complementary to OKAR.
Pentagon ZEBRA is a regular pentagon.
Which of the following statements is most
useful in proving ^SAR is an isosceles
triangle?
Which of the following statements is true?
I.
A.
All sides of ZEBRA are equal in length
by de nition of regular pentagon.
B.
mO1 = mO2 = 72 ; by de nition of regular
pentagon.
C.
mO1 + mO3 = 180 ; by de nition of
supplementary O's on a line.
D.
Quadrilateral PARK is a rhombus
II. Quadrilateral PARK is a square
III. Quadrilateral PARK is a rectangle
A.
I
B.
II
C.
III
D.
II and III
mO3 = mO4; supplements of congruent
O's are congruent.
23.
Can an right triangle and a equilateral triangle
be congruent? Explain your answer.
24.
In quadrilateral ABCD, AD = BC, and AB =
DC. Which of the following statement(s) are
true?
I.
both pairs of opposite angles are
congruent
II. both diagonal bisects each other
III. the diagonals are equal
page 9
A.
II only
B.
III only
C.
I and II
D.
II and III
Midterm Review
25.
ABCD is a parallelogram. E is the midpoint of
AD and F is the midpoint of BC. Prove that
DEBF is a parallelogram.
27.
The drawing shows how to
A.
B.
26.
.
draw the sides of a right triangle
nd the center of a triangle
C.
construct an angle with measure 60
D.
construct an angle with measure 45
The diagram shows a method for constructing
.
28.
The two segments formed as a result of a
.
bisector will always be
A.
the median of a triangle
A.
proportional
B.
congruent
B.
an angle bisector
C.
parallel
D.
perpendicular
C.
the altitude of a triangle
D.
the base of an isosceles triangle
page 10
Midterm Review
29.
Which of the following shows the construction
of a perpendicular from a point to a line?
30.
A.
Which of the following gures shows the
construction of an angle bisector?
A.
B.
B.
C.
C.
D.
D.
page 11
Midterm Review
31.
Besides the information implied by the
! !
!
!
diagram, it is true that BE k CF , and CF ? DF .
How many distinct pairs of parallel lines are
given or implied by the diagram and the
sentence?
A.
32.
B.
2
C.
3
D.
Given the information in the diagram, do the
triangles have to be similar?
4
A.
Yes. The right triangle is 3 times the size
of the left triangle.
B.
Yes. All scalene triangles are similar
C.
No. Side c is not necessarily 24.
D.
No. Scalene triangles are never similar.
The image projected on the screen at a movie
theatre is 50 m wide. If the lm used in the
projector is 50 mm, what is the scale factor of
the projection?
A.
33.
1
34.
1
10
B.
10
C.
100
D.
1000
35.
Which pair of triangles are always similar?
A.
2 scalene
B.
2 equilateral
C.
2 isosceles
D.
2 obtuse
Which of the following statements must be
true?
I.
36.
All isosceles trapezoids are similar.
II. All regular pentagons are similar.
Which of these statements, if true, is su cient
to prove that triangles LMN and NMO are
similar?
III. All parallelograms are similar.
IV. All trapezoids are similar.
A.
I only
B.
II only
C.
IV only
D.
I and II only
page 12
A.
LN = 2 OM
B.
NO bisects LM
C.
OL = OO
D.
OMLN = OMNO
Midterm Review
37.
In the gure, OR = OC.
39.
Which of these statements, if true, is su cient
to prove that triangles CAT and RAM are
similar?
A.
RA ? CM
B.
T is the midpoint of RA
C.
CA = 2 AM
D.
CT + TA = RM + MA
40.
38.
Given that triangle ABC is similar to
triangle DEC, OBAC corresponds to:
A.
OCDE
B.
ODEC
C.
OACB
D.
OECD
page 13
In the gure, DE k BC. Which proportion is
not true?
A.
AD
AE
=
BA
CA
B.
AD
AB
=
AE
AC
C.
DB
BA
=
EC
CA
D.
AD
AE
=
DB
AC
Based on this gure, how many similar
triangles can be identi ed?
A.
2
C.
4
D.
B.
3
cannot be determined
Midterm Review
41.
Complete the following proof.
Given:
AB = BC
D is the midpoint of AB
E is the midpoint of CB
Prove:
AE = DC
statement
reason
1. AB = BC
given
2. DB = 12 (AB)
defn. of midpoint
3. BE = 12 (BC)
defn. of midpoint
4.
both
1
2
of equal lengths
5. mOB = mOB
6.
7. AE = DC
42.
Given:
AE ? DB
CF ? DB
mOBAE = mODCF
Prove:
AB k DC
Statements
Reasons
page 14
Midterm Review
43.
Bisect OABC using a compass and
straightedge.
44. Construct a line through point P perpendicular
to line `.
45.
Bisect the line segment AB.
A
page 15
B
Midterm Review
46.
Given:
LF = KF
LA = KA
Prove:
LJ = KJ
statement
47.
Given:
AB = AC
Prove:
O3 = O4
reason
statement
1. AB = AC
reason
1.
page 16
Midterm Review
48.
Given the gure, how many triangles are
similar to ADG? Name them.
50.
In the diagram, AB = CB and BD bisects AC.
a) Which congruence relationship justi es
that ^ABD = ^CBD ?
b) Why does mOA = mOC ?
49.
RHOM is a rhombus. A, B, C, and D are the
midpoints of each side. Prove that ABCD is a
rectangle.
page 17
Midterm Review