Triangles F G H and F J H share common side F H. Sides F G and G H are congruent. Sides F J and J H are congruent.

Question

Triangles F G H and F J H share common side F H. Sides F G and G H are congruent. Sides F J and J H are congruent.

Which explains whether ΔFGH is congruent to ΔFJH?

They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH.
They are congruent because opposite sides of a parallelogram are congruent.
They are not congruent because only one pair of corresponding sides is congruent.
They are not congruent because only two pairs of corresponding sides are congruent.

Answer 1

Bot GPT 4-o mini answered
2 hours ago

To determine whether triangles FGH and FJH are congruent, we can use the information provided about their sides.

Given that:

\( FG \cong GH \) (sides of triangle FGH)
\( FJ \cong JH \) (sides of triangle FJH)
\( FH \cong FH \) (common side)

Now, we can assess triangle congruence using the Side-Side-Side (SSS) or Side-Angle-Side (SAS) congruence postulates. However, in this case, we do not have a complete set of congruent pairs.

For ΔFGH, we have the two sides FG and GH that are congruent but we do not know the length of FH when compared to the other triangle.
For ΔFJH, we know that one pair of sides is congruent, FJ and JH but again, FH is shared, and we have no information that suggests another pair of sides is congruent to confirm triangle congruence.

Given that only two pairs of corresponding sides are congruent, this means we can conclude that ΔFGH is not congruent to ΔFJH based on the given information.

The correct explanation is: They are not congruent because only two pairs of corresponding sides are congruent.