Question

in the graphic below, $\triangle abc \cong \triangle def$ by:
image of two triangles with side lengths labeled: $\triangle abc$ has sides ab=3, bc=6, ac=8; $\triangle def$ has sides de=3, ef=6, df=8
\bigcirc sss
\bigcirc sas
\bigcirc aaa

Explanation:

Step1: Recall triangle congruence criteria

SSS (Side - Side - Side) congruence states that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
SAS (Side - Angle - Side) requires two sides and the included angle to be equal.
AAA (Angle - Angle - Angle) only guarantees similarity, not congruence.

Step2: Check side lengths

In \(\triangle ABC\), \(AB = 3\), \(BC=6\), \(AC = 8\).
In \(\triangle DEF\), \(DE = 3\), \(EF = 6\), \(DF=8\).
All three pairs of corresponding sides are equal (\(AB = DE\), \(BC = EF\), \(AC = DF\)).

Answer:

SSS