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Geometry
Triangle Congruence Proofs – ASA, AAS
1) Determine which triangles in the figure are congruent by AAS. Write a congruency statement.
Q
R
S
V
T
U
2)
Given: ∠A ≅ ∠X , ∠B ≅ ∠Y , BC ≅ YZ
A
Prove: ∆ABC ≅ ∆XYZ
X
B
C
Y
Z
Decide whether you can use the ASA or AAS Postulate to prove that the triangles below are congruent. If so a)
write the congruence statement and b) identify the postulate. If not, write not possible.
3)
4)
5)
10 m
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10 m
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U
Write a two Column Proof.
6)
Given: SU ≅ TR, SR bisects UT
Prove: ∆SMU ≅ ∆RMT
S
M
R
T
7)
Given: PQ ⊥ QS , RS ⊥ QS , M is the midpoint of PR
Prove: ∆PQM ≅ ∆RSM
R
Q
M
S
P
8)
Given: ∠ ≅ ∠P, MO ≅ LO
Prove: ∆MO ≅ ∆LOP
M
O
P
L
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Write a Two Column Proof or Paragraph Proof.
9)
Given: AE ≅ BD, AE BD, ∠E ≅ ∠D
Prove: ∆AEB ≅ ∆BDC
D
E
.
A
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B
C
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Answer Key
1) ∆QRU ≅ ∆SRU
∠A ≅ ∠X , ∠B ≅ ∠Y , BC ≅ YZ
2)
Given
∠C ≅ ∠Z
if two angles of one triangle are congruent to
two triangles of another, then the third angles are congruent
∆ABC ≅ ∆XYZ ASA
3) AAS
4) Not Possible
5) ASA
6)
SQ ≅ TR
∠U ≅ ∠T
∠S = ∠R
Given
If lines then alternate interior angles are ≅
If lines then alternate interior angles are ≅
SR bisects UT
Given
TM ≅ UM
Definition of segment bisector
∆SMU ≅ ∆RMT
AAS
PQ ⊥ QS , RS ⊥ QS .......... Given
∠Q & ∠S are right angles .......... Def. of ⊥ lines
∠Q ≅ ∠S .......... All right angles are ≅
7) ∠QMP ≅ ∠SMR .......... Vertical Angles are ≅
M is the midpoint of PR .......... Given
PM ≅ RM .......... Definition of midpoint
∆PQM ≅ ∆RSM .......... AAS
8)
∠MO & ∠LOP .......... Vertical Angles are congruent
∠ ≅ ∠P .......... Given
MO ≅ LO .......... Given
∆MO ≅ ∆LOP .......... AAS
AE BD .......... Given
∠A ≅ ∠DBC .......... If lines , then corresponding angles are ≅
9) ∠E ≅ ∠D .......... Given
AE ≅ BD .......... Given
∆AEB ≅ ∆BDC .......... ASA
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