Note that these two triangles share a side length (side GI in the middle), so we can state that GI ≅ GI by the reflexive property (see picture below). What theorem could we use to prove that these triangles are congruent?

Question

Note that these two triangles share a side length (side GI in the middle), so we can state that GI ≅ GI by the reflexive property (see picture below).  What theorem could we use to prove that these triangles are congruent?

GPT-4o mini · Answer

To prove that the two triangles are congruent, you can use the Side-Angle-Side (SAS) Congruence Theorem.

Since you have already established that \( GI \cong GI \) by the reflexive property, you would also need to show that:

Two sides of each triangle (for instance, the sides adjacent to side GI) are congruent.
The angle formed between those two sides (the angle at vertex G and the angle at vertex I, for example) is congruent.

If you can demonstrate these two points in addition to the reflexive property, you can conclude that the two triangles are congruent by the SAS theorem.