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Geo: 4.6 Triangle congruency by ASA, AAS, HL
供稿人: DiLaura
Are these triangles congruent? If so, why?
not congruent, not enough info
Yes, by AAA ∆≅ thm.
Yes, by ASA ∆ ≅ thm
Yes, by AAS ∆ ≅ thm. 
A
B
D
C
Complete the proof.
Given: LM // PO  
and  N is the midpoint of LO
Prove: ∆LMN ≅ ∆OPN
N is the midpoint of LO
∡LNM ≅ ∡ONP
?
∆LMN ≅ ∆OPN
?
Statements
∡L ≅ ∡O
?
LN ≅ ON
LM // PO  
?
not used: 
Def. if midpoint
?
Alternating Interior Angles
ASA ∆ ≅ Thm.
Vertical Angles
?
Given
Given
?
∡M ≅ ∡P
?
Reasons
Given that AB // CD. 
Are these triangles congruent?
not congruent, not enough info
Yes, by AAA ∆≅ thm.
Yes, by ASA ∆ ≅ thm.
Yes, by SAS ∆ ≅ thm.
A
B
E
D
C
Are these triangles congruent?
A
not congruent, not enough info
Yes, HL ∆≅ thm.
Yes, by ASA ∆ ≅ thm.
Yes, by SAS ∆ ≅ thm.
D
B
C
Drag the correct condition that proves the triangle pairscongruent to each other.  
HL ∆≅ Thm
?
Not enough info
?
SAS ∆ ≅ Thm.
?
SSS ∆ ≅ Thm.
?
AAS ∆ ≅ Thm.
?
ASA ∆ ≅ Thm.
?
not used:
7.  True or False.     ΔABC ≅ ΔDBC by the HL ≅ theorem.
TRUE
FALSE
A
C
B
D
8.  True or False.     ΔABC ≅ ΔDBC by the ASA ≅ theorem.
TRUE
FALSE
A
32
C
B
32
D
Complete the proof:
∡Q and ∡S are right angles
R is the midpoint of QS
?
Given: R is the midpoint of QS.∡Q and ∡S are right angles.
Prove:
∆PQR ≅ ∆TSR
?
∡PRQ ≅ ∡TSR
?
Statments
QR ≅ SR
?
∆PQR ≅ ∆TSR
Vertical Angles Thm.
?
Def. of midpoint
not used:  
ASA ∆ ≅ Thm.
?
Given
Given
?
Reasons
HL ∆≅ Thm.
?
10. Drag the correct congruence theorem to the       image that shows how it would be used to prove      the triangles congruent.  For the one that is NOT       used, place it next to the words, "not used".
ASA ≅ theorem
?
HL ≅ theorem
?
SAS ≅ theorem
?
AAS ≅ theorem
?
"not used"
What additional information is needed in order to prove these
triangles are congruent by AAS?
SU ≅ HF
TU ≅ GF
∡U ≅ ∡F
∡T ≅ ∡G
Are these triangles congruent?  If not why not?
Yes, Congruent by AAS
Yes, Congruent by ASA
Yes, Congruent by SSS
No, not congruent, AAA does
not prove triangles congruent. 
What additional information is needed in order to prove thesetriangles are congruent by HL?
SU ≅ HF
TU ≅ GF
∡U ≅ ∡F
∡T ≅ ∡G
What additional information is needed in order to prove these
triangles are congruent by AAS?
SU ≅ HF
TU ≅ GF
∡U ≅ ∡F
∡T ≅ ∡G
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