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1
G.SRT.B.5: Triangle Proofs 1
1 In the diagram of
ABC
and
DEF
below,
AB ≅ DE
,
∠A ≅∠D
, and
∠B ≅∠E
.
Which method can be used to prove
ABC ≅ DEF
?
1) SSS
2) SAS
3) ASA
4) HL
2 As shown in the diagram below,
AC
bisects
∠BAD
and
∠B ≅∠D
.
Which method could be used to prove
ABC ≅ ADC
?
1) SSS
2) AAA
3) SAS
4) AAS
3 In the diagram below of
DAE
and
BCE
,
AB
and
CD
intersect at E, such that
AE ≅ CE
and
∠BCE ≅∠DAE
.
Triangle DAE can be proved congruent to triangle
BCE by
1) ASA
2) SAS
3) SSS
4) HL
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2
4 In the accompanying diagram of
ABC
,
AB ≅ AC
,
BD =
1
3
BA
, and
CE =
1
3
CA
.
Triangle EBC can be proved congruent to triangle
DCB by
1)
S
A
S
≅
S
A
S
2)
A
S
A
≅
A
S
A
3)
S
S
S
≅
S
S
S
4)
H
L
≅
H
L
5 In the accompanying diagram,
HK
bisects
IL
and
∠H ≅∠K
.
What is the most direct method of proof that could
be used to prove
HIJ ≅ KLJ
?
1)
H
L
≅
H
L
2)
S
A
S
≅
S
A
S
3)
A
A
S
≅
A
A
S
4)
A
S
A
≅
A
S
A
6 In the accompanying diagram,
CA⊥AB
,
ED ⊥DF
,
ED AB
,
CE ≅ BF
,
AB ≅ ED
, and
m∠CAB = m∠FDE = 90
.
Which statement would not be used to prove
ABC ≅ DEF
?
1)
S
S
S
≅
S
S
S
2)
S
A
S
≅
S
A
S
3)
A
A
S
≅
A
A
S
4)
H
L
≅
H
L
7 In the accompanying diagram of parallelogram
ABCD,
DE ≅ BF
.
Triangle EGC can be proved congruent to triangle
FGA by
1)
H
L
≅
H
L
2)
A
A
A
≅
A
A
A
3)
A
A
S
≅
A
A
S
4)
S
S
A
≅
S
S
A
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3
8 Parallelogram ABCD with diagonal
DB
is drawn
below. Line segment EF is drawn such that it
bisects
DB
at M.
Which triangle congruence method would prove
that
EMB ∼ FMD
?
1) ASA, only
2) AAS, only
3) both ASA and AAS
4) neither ASA nor AAS
9 In the diagram of quadrilateral ABCD,
AB CD
,
∠ABC ≅∠CDA
, and diagonal
AC
is drawn.
Which method can be used to prove
ABC
is
congruent to
CDA
?
1) AAS
2) SSA
3) SAS
4) SSS
10 In the accompanying diagram of triangles BAT and
FLU,
∠B ≅∠F
and
BA ≅ FL
.
Which statement is needed to prove
BAT ≅ FLU
?
1)
∠
A
≅
∠
L
2)
AT ≅ LU
3)
∠
A
≅
∠
U
4)
BA FL
11 In the diagram below of
AGE
and
OLD
,
∠GAE ≅∠LOD
, and
AE ≅ OD
.
To prove that
AGE
and
OLD
are congruent by
SAS, what other information is needed?
1)
GE ≅ LD
2)
AG ≅ OL
3)
∠
A
G
E
≅
∠
O
L
D
4)
∠
A
E
G
≅
∠
O
D
L
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4
12 Given:
ABE
and
CBD
shown in the diagram
below with
DB ≅ BE
Which statement is needed to prove
ABE ≅ CBD
using only
SAS ≅ SAS
?
1)
∠
C
D
B
≅
∠
A
E
B
2)
∠
A
F
D
≅
∠
E
F
C
3)
AD ≅ CE
4)
AE ≅ CD
13 Given:
AE
bisects
BD
at C
AB
and
DE
are drawn
∠ABC ≅∠EDC
Which statement is needed to prove
ABC ≅ EDC
using ASA?
1)
∠
ABC
and
∠
EDC
are right angles.
2)
BD
bisects
AE
at C.
3)
∠
B
C
A
≅
∠
D
C
E
4)
∠
D
E
C
≅
∠
B
A
C
14 In the diagram below,
AKS
,
NKC
,
AN
, and
SC
are
AN ≅ SC
.
Which additional statement is sufficient to prove
KAN ≅ KSC
by AAS?
1)
AS
and
NC
bisect each other.
2) K is the midpoint of
NC
.
3)
AS ⊥CN
4)
AN SC
15 In the diagram below,
AC
and
BD
intersect at E.
Which information is always sufficient to prove
ABE ≅ CDE
?
1)
AB CD
2)
AB ≅ CD
and
BE ≅ DE
3) E is the midpoint of
AC
.
4)
BD
and
AC
bisect each other.
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5
16 In the diagram of triangles ABD and CBE below,
sides
AD
and
CE
intersect at F, and
∠ADB ≅∠CEB
.
Which statement can not be proven?
1)
A
D
B
≅
C
E
B
2)
∠
E
A
F
≅
∠
D
C
F
3)
A
D
B
∼
C
E
B
4)
E
A
F
∼
D
C
F
17 In parallelogram ABCD shown below, diagonals
AC
and
BD
intersect at E.
Which statement must be true?
1)
AC ≅ DB
2)
∠
A
B
D
≅
∠
C
B
D
3)
A
E
D
≅
C
E
B
4)
D
C
E
≅
B
C
E
18 Kelly is completing a proof based on the figure
below.
She was given that
∠A ≅∠EDF
, and has already
proven
AB ≅ DE
. Which pair of corresponding
parts and triangle congruency method would not
prove
ABC ≅ DEF
?
1)
AC ≅ DF
and SAS
2)
BC ≅ EF
and SAS
3)
∠
C
≅
∠
F
and AAS
4)
∠
CBA
≅
∠
FED
and ASA
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6
19 In the diagram below, four pairs of triangles are
shown. Congruent corresponding parts are labeled
in each pair.
Using only the information given in the diagrams,
which pair of triangles can not be proven
congruent?
1) A
2) B
3) C
4) D
20 Two right triangles must be congruent if
1) an acute angle in each triangle is congruent
2) the lengths of the hypotenuses are equal
3) the corresponding legs are congruent
4) the areas are equal
21 Which condition does not prove that two triangles
are congruent?
1)
S
S
S
≅
S
S
S
2)
S
S
A
≅
S
S
A
3)
S
A
S
≅
S
A
S
4)
A
S
A
≅
A
S
A
22 The diagonal
AC
is drawn in parallelogram ABCD.
Which method can not be used to prove that
ABC ≅ CDA
?
1) SSS
2) SAS
3) SSA
4) ASA
23 Which statements could be used to prove that
ABC
and
A
′
B
′
C
′
are congruent?
1)
AB ≅ A
′
B
′
, BC ≅ B
′
C
′
, and ∠A ≅∠A
′
2)
AB ≅ A
′
B
′
, ∠A ≅∠A
′
, and ∠C ≅∠C
′
3)
∠
A
≅
∠
A
′
,
∠
B
≅
∠
B
′
, and
∠
C
≅
∠
C
′
4) ∠A ≅∠A
′
, AC ≅ A
′
C
′
, and BC ≅ B
′
C
′
24 In
BAT
and
CRE
,
∠A ≅∠R
and
BA ≅ CR
.
Write one additional statement that could be used
to prove that the two triangles are congruent. State
the method that would be used to prove that the
triangles are congruent.
25 In
ABC
,
AB = 5
,
AC = 12
, and
m∠A = 90°
. In
DEF
,
m∠D = 90°
,
DF = 12
, and
EF = 13
. Brett
claims
ABC ≅ DEF
and
ABC ∼ DEF
. Is
Brett correct? Explain why.
ID: A
1
G.SRT.B.5: Triangle Proofs 1
Answer Section
1 ANS: 3
REF: 060902ge
2 ANS: 4
REF: 081114ge
3 ANS: 1
REF: 081210ge
4 ANS: 1
Since is an isosceles triangle and .
REF: 060204b
ID: A
2
5 ANS: 3
Because bisects , and are congruent vertical angles. Since is
given,
AAS ≅ AAS
.
REF: 060420b
6 ANS: 1
Since
and is a transversal, and are alternate interior angles and congruent.
SSS ≅ SSS
REF: 060320b
7 ANS: 3
and are congruent vertical angles. Because ABCD is a parallelogram, and since
Because ABCD is a parallelogram, and since is a transversal,
and
are alternate interior angles and congruent. . This problem can
also be solved using elimination. Since they are not right triangles, HL does not apply, AAA only proves
similarity and SSA does not prove congruence.
REF: 080310b
ID: A
3
8 ANS: 3
REF: 082217geo
9 ANS: 1 REF: 011122ge
10 ANS: 1 REF: 080907b
11 ANS: 2
REF: 081007ge
12 ANS: 3 REF: 081622geo
13 ANS: 3 REF: 011627ge
14 ANS: 4 REF: 081810geo
15 ANS: 4
REF: 061908geo
16 ANS: 1
REF: 012423geo
ID: A
4
17 ANS: 3
. Opposite sides of a parallelogram are congruent and the diagonals of a parallelogram
bisect each other.
REF: 061222ge
18 ANS: 2 REF: 061709geo
19 ANS: 1 REF: 011412ge
20 ANS: 3
1) only proves AA; 2) need congruent legs for HL; 3) SAS; 4) only proves product of altitude and base is equal
REF: 061607geo
21 ANS: 2 REF: 080401b
22 ANS: 3 REF: 080913ge
23 ANS: 2
(2) is AAS, which proves congruency. (1) and (4) are SSA and (3) is AAA.
REF: 010306b
24 ANS:
∠B ≅∠C
and ASA, or
∠T ≅∠E
and AAS, or
AT ≅ RE
and SAS
REF: 011022b
25 ANS:
Yes.
ABC
and
DEF
are both 5-12-13 triangles and therefore congruent by SSS. All congruent triangles are
similar.
REF: 012329geo
