Given that in ∆ABC, AC² = AB² + BC² and ∆LMN is constructed such that LM = AB and ∠LMN = 90°, we can use the Pythagorean theorem.

In right-angled triangle ∆LMN, by the Pythagorean theorem:

�

�

2

=

�

�

2

+

�

�

2

LN

2

=LM

2

+MN

2

Since LM = AB and MN = BC, we can substitute these values:

�

�

2

=

�

�

2

+

�

�

2

LN

2

=AB

2

+BC

2

Now, comparing this with the given condition AC² = AB² + BC², we see that LN = AC.

Therefore, we have AC = LN, and since ∠LMN = 90°, ∆ABC is also a right-angled triangle at B.

Since LM = AB and MN = BC