To determine whether two triangles are congruent based on their side lengths, we can use the Side-Side-Side (SSS) Congruence Postulate.
1. Definition of Congruent Triangles: Two triangles are considered congruent if all three corresponding sides and all three corresponding angles are exactly the same.
2. SSS Congruence Postulate: According to this postulate, if three sides of one triangle are congruent (equal in length) to three sides of another triangle, then the triangles are congruent.
Given this information:
- If we have Triangle ABC and Triangle DEF:
- Side AB is congruent to Side DE.
- Side BC is congruent to Side EF.
- Side CA is congruent to Side FD.
When these three pairs of sides are congruent:
- The sides ensure that the corresponding angles between those sides are also congruent.
- As a result, each angle in Triangle ABC will be equal to the corresponding angle in Triangle DEF.
- This congruence in both sides and angles confirms that Triangle ABC is exactly the same in shape and size as Triangle DEF.
Therefore, based on the SSS Congruence Postulate, two triangles that have three corresponding pairs of congruent sides are guaranteed to be congruent.
So, the correct answer is:
OA. True
