A picture is shown. Within the picture, there are two triangles shown. One is labeled EFG, and the other HIJ. On the line between angles F and E, there are two dashes on it. On the line between G and E, there is one dash on it. On the line between I and J, there is one dash through it. And on the line between H and I, there are once again, two dashes through it.

Question

A picture is shown. Within the picture, there are two triangles shown. One is labeled EFG, and the other HIJ. On the line between angles F and E, there are two dashes on it. On the line between G and E, there is one dash on it. On the line between I and J, there is one dash through it. And on the line between H and I, there are once again, two dashes through it.
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 ∠E≅∠I angle upper E congruent to angle upper I ∠F≅∠I angle upper F congruent to angle upper I ∠G≅∠I angle upper G congruent to angle upper I

GPT-4o mini · Answer

To prove triangles EFG and HIJ are congruent by the SAS Congruence Theorem, we 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.

From the description, we see that the sides EF and HI have two dashes, indicating they are congruent, and side EG and IJ have one dash, indicating they are also congruent.

Therefore, the additional information needed to complete the proof would be:

∠E ≅ ∠I (angle E is congruent to angle I).

This angle is the one included between the two sides we already know are congruent. Thus, confirming that under the SAS Congruence Theorem, triangles EFG and HIJ can be proven congruent.