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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

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

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

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

∠F≅∠I

Answer 1

To apply the SAS (Side-Angle-Side) Congruence Theorem, you need to know that the included angle between the two congruent sides is also congruent. In this case, you already have two pairs of congruent sides (FG ≅ IJ and EF ≅ HI). Therefore, you need the angle between these two sides to be congruent.

The angles in question are ∠F and ∠H, which are the included angles between the congruent sides EF and HI, and FG and IJ, respectively.

So, the additional information needed to prove triangles EFG and HIJ are congruent by the SAS Congruence Theorem is:

∠F≅∠H (angle upper F congruent to angle upper H).