Question

question 40 of 40
which of the following are congruence theorems or postulates? check all that apply.
a. aaa
b. sss
c. ssa
d. aas
e. asa
f. sas

Explanation:

• AAA only proves similarity, not congruence, as triangles can have identical angles but different side lengths.
• SSS (Side-Side-Side): If all three sides of one triangle equal the corresponding sides of another, the triangles are congruent.
• SSA does not guarantee congruence, as it can create two different non-congruent triangles (the ambiguous case).
• AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle equal the corresponding parts of another, the triangles are congruent.
• ASA (Angle-Side-Angle): If two angles and the included side of one triangle equal the corresponding parts of another, the triangles are congruent.
• SAS (Side-Angle-Side): If two sides and the included angle of one triangle equal the corresponding parts of another, the triangles are congruent.

Answer:

B. SSS
D. AAS
E. ASA
F. SAS