Download Triangle Congruence and Similarity Review Score Name: Date

Triangle Congruence and Similarity Review
Score
Name:
Date:
Show all work for full credit.
1.
2.
3.
In a plane, lines that never meet are
called
.
A.
parallel
B.
perpendicular
C.
congruent
D.
intersecting
E.
concentric
In the drawing, what is the measure of angle
y?
The two angles formed as a result of a
.
bisector will always be
A.
complementary
B.
supplementary
C.
right
D.
congruent
A.
A line segment has A and B as its endpoints
and M as its midpoint. If A has coordinates
(h; 0) and B has coordinates (0; m), what are
the coordinates of M ?
A.
D.
4.
5.
h m
;
2 2
(h; m)
B.
( h; 2m)
E.
( h; m)
C.
40
B.
60
C.
80
D.
100
6.
Solve for x and y. Show all work.
7.
Which of the following sets of points are
collinear?
(2h; m)
!
!
In the gure, AB is parallel to CD and OBDC
is right. Which of the following statements
may be false?
A.
AB ? BD
B.
measure of O3 is less than 90
C.
O2 and O 4 are supplementary
D.
O1 and O 3 are congruent
page 1
A.
A, B, D
B.
A, B, C
C.
B, D, C
D.
D, A, C
E.
C, A, D
8.
Lines t1 , t2 , and t3 are parallel lines intersected
by line t4 . What is the measure of Os?
A.
42
B.
48
C.
D.
Not enough information.
12.
Which type of triangle is ^ABC ?
A.
Right
B.
Isosceles
C.
Scalene
D.
Equilateral
138
13.
Given the gure and the following information:
AN k SK and AS k NK
9.
Find x.
mOA = 5x + 6
mODAS = 3x + 50
mON = 3y
A.
10.
11.
Score
50
B.
80
C.
110
D.
10
Find the value of x and y.
120
In the diagram, what is the sum of the
measures of OB and OD?
A.
90
B.
95
C.
102.5
D.
112.5
E.
142.5
In the gure below, what is the measure of
OB ?
A.
35
B.
40
C.
71
D.
76
E.
105
page 2
Triangle Congruence and Similarity Review
14.
In the gure, lines B and C are parallel.
alternate interior
adjacent
alternate exterior
corresponding
supplementary
16.
BC = 4. Proof the triangles are similar.
vertical
Statements
complementary
Reason
a) Use the terms in the box to label each
angle pair. More than one term may
apply to each angle pair.
O1, O2
O2, O4
O3, O 5
O2, O 6
b) If mO3 = 9x and mO8 = 6x, nd the
measure of each numbered angle in the
gure.
17.
15.
Score
In the diagram, if lines a and b are parallel,
which of the following must be true?
A.
O2 = O5
B.
O3 = O4
C.
O7 = O1
D.
O4 = O5
E.
O8 = O2
Given:
AD bisects BC
AE = DE
Prove:
AB k CD
Statements
Reason
Flowchart Proof:
page 3
Triangle Congruence and Similarity Review
19.
18.
Given:
CF = EF
FD is a median of ^CFE
Given:
AD is the perpendicular bisector of BC
Prove:
^ABC is isosceles
Statement
Prove:
CD = ED
Two-Column Proof:
given
2.
def'n of ? bisector
3.
def'n of ? bisector
4.
Statements
Reason
1. AD is ? bisector of BC
All right angles are congruent
5. AD = AD
Reason
6. ^ABD = ^ ACD
7. AB = AC
SAS
8. ^ABC is isosceles
Fill in the blanks. Then write a owchart
proof.
Paragraph Proof:
Score
page 4
Triangle Congruence and Similarity Review
22.
20.
Given:
AB k DC
AB = DC
Prove:
mODAC = mOBCA
To test this conjecture, which pair of congruent
angles are alternate interior angles?
Two Column Proof:
Paragraph Proof:
Statements
Reasons
23.
Flowchart Proof:
21.
The Corresponding Angles Conjecture states
that if two parallel lines are cut by a
transversal, the alternate interior angles are
congruent. The picture below shows this
relationship.
The Corresponding Angles Conjecture states
that if two parallel lines are cut by a
transversal, the corresponding angles are
congruent. The picture below shows this
relationship.
24.
A.
O1 and O4
B.
O2 and O8
C.
O4 and O8
D.
O3 and O5
Which of these pairs of triangles must be
similar?
A.
two right triangles where the length of
each hypotenuse is 3
B.
two acute triangles with two pairs of
corresponding, congruent sides
C.
two right triangles, one whose sides are
in the ratio 3 : 4 : 5 and the other 5 : 12 : 13
D.
two triangles, one with sides x, y and z,
and the other with sides 2x, 2y, and 2z
Given:
ST k QR
Prove:
^PST
^PQR
Which of these congruent angles are
corresponding angles?
Score
A.
O1 and O 4
B.
O1 and O3
C.
O4 and O 8
D.
O4 and O3
page 5
Triangle Congruence and Similarity Review
25.
In the gure shown, segment AC is
perpendicular to segment BC in triangle ACB.
Segment FE is parallel to segment BC. If
AF = 12, FB = 8 and FE = 9,
a) What is the length of segment BC?
b) Why is segment FE perpendicular to
segment AC?
26.
Given:
SQ = TR, OPST = OPTS
Prove:
^PQR is isosceles.
Statements
Score
Reasons
page 6
Triangle Congruence and Similarity Review
27.
Given that triangle ABC is similar to
triangle DEC, OABC corresponds to:
A.
OCDE
B.
ODEC
C.
OACB
D.
OECD
28.
29.
30.
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
In the gure, TU k QR. Which proportion is
not true?
A.
TU
QR
=
RS
US
B.
QR
TU
=
QS
TS
C.
RU
US
=
QR
TU
D.
ST
SQ
=
TU
QR
In the diagram, mOD = OE. Which of the
following statements are true for this diagram?
I.
^ADC
^BEC
II. ^ADC
^EBC
III. AD k BE
Score
page 7
A.
I only
B.
II only
C.
III only
D.
I and II
E.
I and III
Triangle Congruence and Similarity Review
31.
35.
In the diagram, CD ? AC, BE ? AC, AE = 17,
BE = 8, and CD = 32. Find DE.
A.
35
B.
45
D.
60
E.
68
C.
51
36.
32.
33.
A.
16
B.
17
C.
19
D.
20
E.
21
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.
PQ is parallel to XY . What is the length of
XY in centimeters?
A.
6
B.
5 31
C.
4
D.
3
E.
2
In the diagram, AD = DC, DE k AB, and
DE = 4. Find AB.
A.
2
B.
4
C.
6
D.
8
E.
16
37.
34.
Find the length of side x.
Collin wants to nd the width of a creek. He
takes some measurements and creates a
diagram.
In the diagram, DE k AB, CA = 9, DA = 3, and
CE = 10. Find EB.
A.
2.5
B.
3
C.
4
D.
4.5
E.
5
38. V and Y are midpoints of TW and TX , and
U and Z are midpoints of TV and TY . If
VY = 7, nd the length of UZ .
A.
3.5
B.
14
C.
21
D.
10.5
Assuming that AC is perpendicular to CD and
CD is parallel to BE, what is the width of the
creek to the nearest meter? Show all your
work.
Score
page 8
Triangle Congruence and Similarity Review
39.
Two Column Proof:
Paragraph Proof:
Statements
Reasons
40.
Two Column Proof:
Paragraph Proof:
Statements
Flowchart Proof:
Reasons
Flowchart Proof:
Score
page 9
Triangle Congruence and Similarity Review
42.
Fill in the reasons for the proof.
Given:
AC is the median to BE
EC is the median to AD
Prove:
41.
Given:
VT bisects RW
RW bisects TV
Prove:
^RSV = ^WST
statement
1.
2.
3.
4.
5.
6.
7.
8.
Two Column Proof:
Paragraph Proof:
Statements
AB k ED
Reasons
reason
AC is the median to BE
BC = CE
mO1 = mO2
EC is the median to AD
AC = CD
^ACB = ^DCE
mO3 = mO4
AB k ED
Flowchart Proof:
Score
page 10
Triangle Congruence and Similarity Review