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

Question

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

GPT-4o mini · Answer

To prove triangles EFG and HIJ are congruent by the SAS (Side-Angle-Side) Congruence Theorem, you need to show that two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

Based on the options provided, to apply SAS, you would need:

Two pairs of congruent sides: e.g., EF ≅ HI and FG ≅ IJ.
The angle included between these two sides in both triangles must also be congruent.

From the given options, we need to identify an angle that is included between the pairs of congruent sides.

If you have already established:

EF ≅ HI
FG ≅ IJ

Then you would need to demonstrate that the angle between those sides, which is ∠F in triangle EFG and ∠H in triangle HIJ, is congruent:

∠F ≅ ∠H

This would give us the necessary information to apply the SAS Congruence Theorem.

The correct choice from your list is ∠F ≅ ∠H. However, if that option does not appear, please verify which sides' arrangements and any additional included angles fit your triangle setup.