To determine if two triangles that have the same side lengths are always congruent, let's consider a fundamental geometry principle:
Side-Side-Side (SSS) Congruence Postulate:
- This postulate states that if three sides of one triangle are congruent (equal in length) to three sides of another triangle, then the two triangles are congruent.
Here's the reasoning in detail:
1. Triangle Definition:
- A triangle is a geometric figure with three sides and three angles.
2. Congruence Definition:
- Two triangles are congruent if their corresponding sides and angles are exactly equal.
3. SSS Congruence Postulate:
- According to the SSS Congruence Postulate, if all three sides of one triangle are the same lengths as all three sides of another triangle, then these triangles are congruent.
- This means that not only are the side lengths the same, but the angles between corresponding sides must also be the same. Thus, the triangles are identical in shape and size.
4. Application:
- Given two triangles, if we know that their corresponding sides are equal in length:
- Side [tex]\(AB = DE\)[/tex]
- Side [tex]\(BC = EF\)[/tex]
- Side [tex]\(CA = FD\)[/tex]
- Based on the SSS Congruence Postulate, these triangles must be congruent.
Thus, considering the SSS Congruence Postulate, the statement "Two triangles that have the same side lengths will always be congruent" is indeed true.
Therefore, the correct answer is:
A. True
