Answer: The correct option are 1 and 4 .
Explanation:
It is given that [tex]\Delta ABC\cong \Delta LMN[/tex], it means AB = LM, BC=MN, AC=LM, [tex]\angle A=\angle L[/tex], \angle B=\angle M and \angle C=\angle N as shown in the figure.
All the possible way to write [tex]\Delta ABC\cong \Delta LMN[/tex] is given below,
[tex]\Delta ABC\cong \Delta LMN[/tex]
[tex]\Delta ACB\cong \Delta LNM[/tex]
[tex]\Delta BAC\cong \Delta MLN[/tex]
[tex]\Delta BCA\cong \Delta MNL[/tex]
[tex]\Delta CAB\cong \Delta NLM[/tex]
[tex]\Delta CBA\cong \Delta NML[/tex]
So, the correct options are 1 and 4.
According to the second[tex]\Delta CBA\cong \Delta MNL[/tex], it means [tex]\angle C=\angle M[/tex] and [tex]\angle B=\angle N[/tex] which is not exactly true, therefore it is not a correct option.
According to the second[tex]\Delta BCA\cong \Delta NML[/tex], it means [tex]\angle C=\angle M[/tex] and [tex]\angle B=\angle N[/tex] which is not exactly true, therefore it is not a correct option.
