Download Congruent Triangles Name: Date: 1. In the accompanying diagram

Congruent Triangles
Name:
1.
Date:
In the accompanying diagram, B is the midpoint
of AC, DA ? AC, EC ? AC, and DB = EB.
Which method of proof may be used to prove
^DAB = ^ECB ?
4.
A.
SAS = SAS
A.
HL = HL
B.
ASA = ASA
B.
SSS = SSS
C.
HL = HL
C.
ASA = ASA
D. SAS = SAS
D. AAS = AAS
2.
In the accompanying diagram, ^ABC and ^RST
are right triangles with right angles at B and S,
respectively; AB = RS and AC = RT.
5.
Which statement can be used to justify that
^ABC = ^RST ?
A.
SAS = SAS
B.
C.
HL = HL
D. SAA = SAA
In the accompanying diagram, PR = SQ, PR ? RQ,
and SQ ? RQ. Which statement can be used to
prove that ^PQR = ^SRQ ?
A.
AAS = AAS
B.
SAS = SAS
C.
HL = HL
D. SSS = SSS
ASA = ASA
6.
3.
In the accompanying diagram of quadrilateral
ABCD, diagonal AC bisects OBAD and OBCD.
Which statement can be used to prove that
^ABC = ^ADC ?
Two triangles are congruent if
In the accompanying diagram of quadrilateral
QRST, RS = ST, SR ? QR, and ST ? QT.
Which method of proof may be used to prove
^QRS = ^QTS ?
A.
corresponding angles are congruent
A.
HL
B.
B.
corresponding sides and corresponding angles
are congruent
C.
AAS
D. ASA
C.
the angles in each triangle have a sum of
180
D. corresponding sides are proportional
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SAS
7.
10.
In the accompanying diagram, RL ? LP, LR ? RT,
and M is the midpoint of TP. Which method
could be used to prove ^ TMR = ^PML ?
A.
SAS = SAS
B.
AAS = AAS
C.
HL = HL
Which statement can be used to prove
^STY = ^ DTU?
D. SSS = SSS
8.
11.
!
! !
In the accompanying diagram, ACE, BCD, AB,
!
and DE, OA = OE, and C is the midpoint of AE.
Which theorem justi es ^ABC = ^EDC ?
A.
SSS = SSS
B.
SAS = SAS
C.
ASA = ASA
In the accompanying diagram, point T is the
midpoint of SD and YU; SY and UD are drawn.
A.
SSS = SSS
B.
C.
ASA = ASA
D. HL = HL
SAS = SAS
In the accompanying diagram, E is the midpoint
of AB and CD.
D. SSA = SSA
Triangle AEC can be proved congruent to triangle
BED by
9.
In the accompanying diagram of isosceles
triangle ABC, OACB is the vertex angle, CM ? AB,
and M is the midpoint of AB.
Which statement can not be used to justify
^ACM = ^BCM ?
A.
HL = HL
B.
AAS = AAS
C.
SSS = SSS
12.
A.
AAS = AAS
B.
C.
SAS = SAS
D. SSS = SSS
ASA = ASA
In the accompanying diagram, AB and CD intersect
at E, E is the midpoint of AB, and OA = OB.
Which statement can be used to prove
^ADE = ^BCE
D. AAA = AAA
page 2
A.
ASA = ASA
B.
C.
SSS = SSS
D. SAS = SAS
HL = HL
Congruent Triangles
13.
15.
In the accompanying diagram, HK bisects IL and
OH = OK.
In the diagram of ^ABC and ^DEF below,
AB = DE, OA = OD, and OB = OE.
What is the most direct method of proof that
could be used to prove ^HIJ = ^KLJ?
A.
HL = HL
B.
C.
AAS = AAS
D. ASA = ASA
Which method can be used to prove
^ABC = ^DEF?
SAS = SAS
A.
16.
14.
In the accompanying diagram of triangles BAT
and FLU, O B = OF and BA = FL.
SSS
B.
SAS
C.
ASA
D. HL
If ^JKL = ^MNO, which statement is always
true?
A.
OKLJ = ONMO
B.
C.
JL = MO
D. JK = ON
OKJL = O MON
Which statement is needed to prove
^BAT = ^ FLU?
17.
A.
OA = OL
B.
C.
OA = OU
D. BA k FL
In the diagram below, ^ABC = ^XYZ.
AT = LU
Which statement must be true?
page 3
A.
OC = O Y
B.
C.
AC = YZ
D. CB = XZ
OA = OX
Congruent Triangles
18.
As shown in the diagram below, AC bisects OBAD
and OB = OD.
20.
In the diagram below of ^DAE and ^BCE, AB
and CD intersect at E, such that AE = CE and
OBCE = ODAE.
Which method could be used to prove
^ABC = ^ADC?
A.
SSS
B.
AAA
C.
SAS
Triangle DAE can be proved congruent to
triangle BCE by
D. AAS
A.
19.
21.
The diagram below shows a pair of
congruent triangles, with OADB = OCDB and
OABD = O CBD.
ASA
B.
SAS
C.
SSS
D. HL
In the diagram below, four pairs of triangles are
shown. Congruent corresponding parts are labeled
in each pair.
A
C
B
D
Which statement must be true?
A.
OADB + OCBD
B.
OABC + OADC
C.
AB = CD
D. AD = CD
Using only the information given in the diagrams,
which pair of triangles can not be proven
congruent?
A.
page 4
A
B.
B
C.
C
D. D
Congruent Triangles
22.
In the accompanying diagram of isosceles
triangle ABC, AB = BC, mOBAC = x, and
mOABC = x + 30.
25.
What is the value of x ?
A.
80
B.
C.
50
D. 30
The accompanying diagram shows the roof of a
house that is in the shape of an isosceles triangle.
The vertex angle formed at the peak of the roof is
84 .
75
What is the measure of x?
23.
A.
In the diagram below of ^ABC, AB = AC,
mOA = 3x, and mOB = x + 20.
138
B.
96
C.
84
D. 48
26.
In the accompanying diagram of ^ABC, CB = CA,
is extended to D, and mOB = 42. Find mOCAD.
27.
In the accompanying diagram of isosceles triangle
SUM, SM = UM and OMUD is an exterior angle
formed by extending SU to D. If mOMUD = 124,
nd mOM.
What is the value of x?
A.
24.
10
B.
28
C.
32
D. 40
In the accompanying diagram, isosceles ^ABC =
isosceles ^DEF, mOC = 5x, and mO D = 2x + 18.
Find mOB and mOBAG.
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Congruent Triangles
28.
Given that ABCD is a parallelogram, a student wrote the proof below to show that a pair of its opposite angles are
congruent.
Statement
Reason
1. ABCD is a parallelogram.
1. Given
3. AC = CA
3. Re exive Postulate of Congruency
2. BC = AD
AB = DC
4. ^ABC = ^CDA
5. OB = OD
2. Opposite sides of a parallelogram
are congruent.
4. Side-Side-Side
5.
What is the reason justifying that OB = OD?
A.
Opposite angles in a quadrilateral are congruent.
B.
Parallel lines have congruent corresponding angles.
C.
Corresponding parts of congruent triangles are congruent.
D. Alternate interior angles in congruent triangles are congruent.
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Congruent Triangles