Question

which shows two triangles that are congruent by the sss congruence theorem?

Explanation:

1. Recall SSS (Side - Side - Side) congruence: Three pairs of corresponding sides must be equal.
2. Analyze each option:

• First option: Likely involves right angles (HL or SAS), not SSS.
• Second option: In \( \triangle ABC \) and \( \triangle EDC \), we have two marked equal sides in each triangle, and \( AC = EC \) (since \( A - C - E \) is a straight line, so \( AC+CE \) is the total length, but here \( AC = EC \) by the diagram's structure, and the other two pairs of sides are marked equal. So three sides correspond: \( AB = ED \), \( BC = DC \), \( AC = EC \), satisfying SSS.
• Third option: Involves angles (ASA or SAS), not SSS.
• Fourth option: Only two sides and a non - included angle or partial markings, not SSS.

Answer:

The second option (with triangles \( \triangle ABC \) and \( \triangle EDC \) sharing point \( C \) on line \( AE \), and two pairs of marked equal sides in each triangle, plus \( AC = EC \) by segment addition, satisfying SSS).