Final answer:
Triangles ∆FGH and ∆FJH cannot be determined to be congruent with the information provided as only two pairs of corresponding sides are mentioned to be congruent without information about the congruent angles or the use of a specific congruence postulate.
Step-by-step explanation:
To determine whether ∆FGH is congruent to ∆FJH, we should consider the congruent sides presented: GH ≅ GF, JF ≅ JH, and FH ≅ FH. By the definition of congruence in triangles, they are congruent if all their corresponding sides and angles are congruent. In this case, we have only been provided information about the sides.
The statement 'They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH' suggests that two pairs of corresponding sides are congruent and they share a common side FH, making it seem like there's enough information to assert congruence. However, without knowing whether the corresponding angles are congruent or without applying a congruence postulate or theorem such as SSS (side-side-side), SAS (side-angle-side), ASA (angle-side-angle), AAS (angle-angle-side), or HL (hypotenuse-leg for right triangles), we cannot confirm the triangles are congruent.
Given this, the statement 'They are not congruent because only two pairs of corresponding sides are congruent' would make more sense, but it neglects the fact that there is also a common side FH. Thus, neither of the statements provided are completely accurate without additional information about the corresponding angles or without stating which congruence postulate is used. Therefore, with the information given, we cannot conclude they are congruent solely based on the fact that two pairs of corresponding sides are congruent and they share a common side.