Bot GPT 4-o mini To determine which congruence theorem can be used to prove that triangles \( \triangle BDA \) and \( \triangle BDC \) are congruent, let's look at the information given.
- Shared Side: The triangles share side \( BD \).
- Congruent Sides: Sides \( BA \) and \( BC \) are congruent, so \( BA \cong BC \).
- Congruent Sides: Sides \( AD \) and \( DC \) are congruent, so \( AD \cong DC \).
From this information, we note the following:
- You have two sides that are equal from each triangle (\( BA \cong BC \) and \( AD \cong DC \)).
- You have included the side \( BD \) which is common to both triangles.
This combination meets the criteria for the Side-Side-Side (SSS) congruence theorem, which states that if three sides of one triangle are respectively equal to three sides of another triangle, then the two triangles are congruent.
Therefore, the correct congruence theorem to use in this case is:
SSS (Side-Side-Side).
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