The statements that are true for triangle LMN are the 1st, 2nd and fourth options. That is
[] The side opposite ∠L is NM.
[] The side opposite ∠N is ML.
[] The hypotenuse is LN.
The question as well as the accurate diagram is shown in the attachment below.
To determine which statements are true for triangle LNM, we will observe each of the options one after the other.
- For the first option - [] The side opposite ∠L is NM
In the diagram, the side opposite angle L is side NM
∴ The statement "The side opposite ∠L is NM" is true
- For the second option - [] The side opposite ∠N is ML
In the diagram, the side opposite angle N is side ML
∴ The statement "The side opposite ∠N is ML" is true
- For the third option - [] The hypotenuse is NM
In a right triangle, the hypotenuse is the longest side. It is the side opposite the right angle.
In the diagram, NM is not the side opposite the right angle. LN is the side opposite the right angle.
∴ The statement "The hypotenuse is NM" is not true
- For the fourth option - [] The hypotenuse is LN
As stated above, LN is the side opposite the right angle. That is, LN is the hypotenuse.
∴ The statement "The hypotenuse is LN" is true
- For the fifth option -[] The side adjacent ∠L is NM
The side adjacent an angle is the side next to it.
In the diagram, side NM is not adjacent to angle L, it is opposite to angle L.
∴ The statement "The side adjacent ∠L is NM" is not true
- For the sixth option - [] The side adjacent ∠N is ML
In the diagram, side ML is not adjacent to angle N, it is opposite to angle N.
∴ The statement "The side adjacent ∠N is ML" is not true
Hence, the statements that are true for triangle LMN are the 1st, 2nd and fourth options. That is
[] The side opposite ∠L is NM.
[] The side opposite ∠N is ML.
[] The hypotenuse is LN.
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