What additional information is needed in order to prove triangles EFG and HIJ are congruent by the SAS Congruence Theorem? (1 point) Responses ∠E≅∠I angle upper E congruent to angle upper I ∠F≅∠I angle upper F congruent to angle upper I ∠F≅∠H angle upper F congruent to angle upper H ∠G≅∠I angle upper G congruent to angle upper I Skip to navigation

Question

GPT-4o mini · Answer

To prove that triangles EFG and HIJ are congruent by the SAS (Side-Angle-Side) Congruence Theorem, you need two sides and the angle that is included between those sides to be congruent in both triangles.

Assuming you already have information about the lengths of two sides in each triangle being congruent (e.g., EF ≅ HI and FG ≅ IJ), you would need more information on the angle that is included between those two sides.

Therefore, you would need to establish that:

Angle ∠F is congruent to an angle in triangle HIJ (most likely ∠H or ∠I).

Thus, the correct response from the options given would be the one that states the congruence of the angle that is included between the two congruent sides. In the context of the options:

If you need Angle ∠F to have a congruence with either ∠H or ∠I (most typically, one of these), that would allow you to apply the SAS theorem effectively.

So based on your response options, choose the one that indicates the congruence of Angle F with either Angle H or Angle I.

Answer

which one

GPT-4o mini · Answer

To apply the SAS Congruence Theorem for triangles \( EFG \) and \( HIJ \), you need to establish congruence for two sides and the included angle. Given the options you provided:

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

The most relevant option that would help prove that triangles \( EFG \) and \( HIJ \) are congruent by SAS is:

\( \angle F \cong \angle H \)

This is because \( \angle F \) (the included angle between sides \( EF \) and \( FG \) in triangle \( EFG \)) must be congruent to \( \angle H \) in triangle \( HIJ \) for the SAS theorem to be applied correctly along with the congruent sides.

So, the correct answer is \( \angle F \cong \angle H \).