Geo 4.5: Congruent Triangles SSS & SAS
1. Tell if and why the triangles are congruent.
Not congruent, not enough info
∡A ≅ ∡C, thus ∆'s are ≅ by SAS ∆≅ Thm.
.
 ∆'s are ≅ by the definition of ≅∆'s 
A
B
D
C
2. Tell if and why the triangles are congruent.
Not congruent, not enough info
AB ≅ CB, thus ∆'s are ≅ by SSS ∆≅ Thm.
BD ≅ BD, thus ∆'s are ≅, by SAS ∆≅ Thm.
 ∆'s are ≅ by the definition of ≅∆'s 
A
B
D
C
3. Tell what the value x must be in order for the two triangles to be congruent by SSS ∆ ≅ Thm.
6x - 4
B
x = 
A
C
4x + 7
D
4. Tell if and how the two triangles are congruent.
C
A
Not congruent, not enough info
AC ≅ED, thus ∆'s are ≅ by SSS ∆≅
 ∡ABC ≅∡EBD, thus ∆'s are ≅ by SAS ∆≅
B
D
E
5.  Which additional information is needed to prove       ΔABC ≅ ΔCDE by SAS Δ ≅ theorem?  
A
C
E
B
∡B ≅ ∡D
AB ∕∕ CD
CB ≅ ED
D
6.  What additional information is needed to prove
     ΔABC ≅Δ EBD by SSS Δ ≅ theorem?
B is the midpoint of CD
AC ∕∕ ED
C
A
B
AC ≅ ED
∡CBA ≅ ∡DBE
D
E
7.  Which congruence theorem or definition would 
     you use to prove these triangles congruent?
SSS Δ ≅ theorem
W
definition of ≅ Δ's
S
O
SAS Δ ≅ theorem
N
Not enough information
to prove triangles congruent
?
Tell which statement is true for the following pairs of triangles. 
Triangles congruent by SAS ∆≅ Thm.
?
Congruent triangles
by SSS ∆≅ Thm.
?
9.  Could you use SSS or SAS to prove ΔSNO ≅ ΔOWS?
W
S
YES
NO
O
N
10. Tell if and how the two triangles are congruent.
C
A
Not congruent, not enough info
AB ≅ EB, thus ∆'s are ≅ by SSS ∆≅
AB ≅ EB and AC ≅ ED, thus ∆'s are ≅     by SSS ∆≅
B
D
E
Congruent by SSS∆≅ Thm.
?
Identify which statement is true for each of the pairs of 
triangles below. 
Congruent by SAS ∆≅Thm.
?
Not enough info to 
prove triangles congruent.
?
What additional information is needed to prove these 
triangles are congruent by SAS ∆≅ Thm.
RS ≅ PQ
RO ≅ OQ
∡P ≅ ∡S
∡R ≅ ∡Q
Complete the proof by 
dragging the correct statements
and reasons to their locations. 
Prove: ∆QAB ≅ ∆PBA
∆QAB ≅ ∆PBA 
?
∡QAB ≅ ∡PBA
Statements 
AQ ≅ BP
?
AB ≅ AB
Reflexive Property of ≅
?
SAS ∆ ≅ Thm.
?
Given
Given
?
Reasons
not used: 
SSS ∆≅ Thm.
?
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