Use the image to answer the question.

Question

An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side F G is congruent to side I J. Side E F is congruent to side H I.

What additional information is needed in order to prove triangles EFG and HIJ are congruent by the SAS Congruence Theorem?

(1 point)
Responses

∠F≅∠H
angle upper F congruent to angle upper H

∠F≅∠I
angle upper F congruent to angle upper I

∠G≅∠I
angle upper G congruent to angle upper I

∠E≅∠I
angle upper E congruent to angle upper I

Answer 1

To use the SAS (Side-Angle-Side) Congruence Theorem, we need to have two pairs of congruent sides and the included angle between those sides must also be congruent.

From the information given, we know that:

• Side \( FG \) is congruent to side \( IJ \).
• Side \( EF \) is congruent to side \( HI \).

To prove triangles \( EFG \) and \( HIJ \) congruent by SAS, we need to establish the congruence of the included angle \( \angle EFG \) and \( \angle HIJ \) (the angles between the two pairs of congruent sides).

Among the choices provided:

• \( \angle F \cong \angle H \)
• \( \angle F \cong \angle I \)
• \( \angle G \cong \angle I \)
• \( \angle E \cong \angle I \)

To ensure that we have the necessary congruency of angles between the two sets of sides, we need:

∠F ≅ ∠H

This angle would act as the included angle necessary to apply the SAS Congruence Theorem.

So, the correct answer is:

∠F≅∠H.