The flowchart proof of the congruence:
Given: AB = LM, BZ = MN, and AZ = LN.
Reason: SSS congruence criterion.
Conclusion: triangle ABZ ≅ triangle LMN.
The congruence of triangles ABZ and LMN is established through the Side-Side-Side (SSS) congruence criterion, indicating that all corresponding sides of the triangles are of equal length.
In triangle ABZ, the side lengths are as follows: AB = 6, BZ = 4, and AZ = 8. Simultaneously, in triangle LMN, the corresponding sides are LM = 8, MN = 6, and LN = 4.
By satisfying the SSS congruence criterion, these triangles demonstrate a one-to-one correspondence in side lengths.
This congruence implies that the triangles are identical in shape and size, with the same internal angles.
Mathematically, the SSS congruence criterion is expressed as follows: if the three sides of one triangle are equal to the corresponding three sides of another triangle, the triangles are congruent.
In the case of ABZ and LMN, the sides AB, BZ, and AZ match precisely with the sides LM, MN, and LN, respectively.
Consequently, based on the SSS congruence criterion, we can conclusively affirm that triangle ABZ is congruent to triangle LMN.
This congruence establishes a geometric equivalence between the two triangles, reflecting their shared side lengths and confirming their identical shapes and sizes.