consider $\triangle lnm$.
which statements are true for triangle lnm? check all that apply.
$\square$ the side opposite $\angle l$ is $\overline{nm}$.
$\square$ the side opposite $\angle n$ is $\overline{ml}$.
$\square$ the hypotenuse is $\overline{nm}$.
$\square$ the hypotenuse is $\overline{ln}$.
$\square$ the side adjacent $\angle l$ is $\overline{nm}$.
$\square$ the side adjacent $\angle n$ is $\overline{ml}$.

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# Brief Explanations:
1. For "The side opposite ∠L is $\overline{NM}$": In a triangle, the side opposite an angle is the one not connected to the angle's vertex. ∠L is at vertex L, so the side opposite is $\overline{NM}$ (connecting M and N, not L), so this is true.
2. For "The side opposite ∠N is $\overline{ML}$": ∠N is at vertex N, the side opposite should be $\overline{ML}$ (connecting M and L, not N), so this is true.
3. For "The hypotenuse is $\overline{NM}$": In a right triangle, the hypotenuse is the side opposite the right angle. The right angle is at M, so the hypotenuse should be $\overline{LN}$, not $\overline{NM}$, so this is false.
4. For "The hypotenuse is $\overline{LN}$": Since the right angle is at M, the hypotenuse is the side opposite (LN), so this is true.
5. For "The side adjacent ∠L is $\overline{NM}$": Adjacent sides to an angle in a right triangle (other than hypotenuse) are the legs connected to the angle. ∠L is at L, connected to ML and LN. Wait, no—wait, in right triangle at M, ∠L is at L, the adjacent sides would be ML (one leg) and the other leg? Wait, no, let's re - check. ∠L: the sides forming ∠L are ML and LN. The side adjacent (non - hypotenuse) would be ML? Wait, no, the first statement: side opposite ∠L is NM (correct). Then adjacent to ∠L: the sides that form ∠L are ML and LN. But NM is opposite. Wait, maybe I made a mistake earlier. Wait, ∠L: in triangle LNM, right - angled at M. So vertices: L, N, M with right angle at M. So ∠L is at L, between sides ML and LN. So the side opposite ∠L is NM (correct). The side adjacent to ∠L: ML (since ML is one of the sides forming ∠L, and it's a leg, not the hypotenuse). Wait, the option says "The side adjacent ∠L is $\overline{NM}$"—no, NM is opposite. Wait, maybe I messed up. Wait, let's re - evaluate each:

Wait, let's list the sides:

- Legs: ML (horizontal) and NM (vertical), hypotenuse LN (the slant side).

∠L: at L, between ML and LN. So the side opposite ∠L is NM (correct, as NM doesn't touch L). The side adjacent to ∠L: ML (since ML is connected to L and is a leg). But the option says "The side adjacent ∠L is $\overline{NM}$"—that's wrong. Wait, maybe I made a mistake in the first analysis.

Wait, let's start over:

1. Side opposite ∠L: ∠L is at L. The sides of the triangle are ML, NM, LN. The side not connected to L is NM (since ML is connected to L, LN is connected to L). So side opposite ∠L is NM: true.

2. Side opposite ∠N: ∠N is at N. Sides: MN, LN, ML. The side not connected to N is ML (MN is connected to N, LN is connected to N). So side opposite ∠N is ML: true.

3. Hypotenuse: right angle at M, so hypotenuse is LN (opposite right angle), so "hypotenuse is NM" is false.

4. Hypotenuse is LN: true.

5. Side adjacent ∠L: ∠L is at L, the sides forming ∠L are ML and LN. The adjacent side (other than hypotenuse) would be ML (since LN is hypotenuse). The option says "The side adjacent ∠L is $\overline{NM}$"—NM is opposite, so this is false.

6. Side adjacent ∠N: ∠N is at N, sides forming ∠N are MN and LN. The adjacent side (other than hypotenuse) would be MN (or NM, same segment). Wait, the option says "The side adjacent ∠N is $\overline{ML}$"—ML is opposite ∠N, so this is false. Wait, maybe I made a mistake here. Wait, ∠N is at N, the sides adjacent to ∠N are MN (NM) and LN? No, in triangle, adjacent sides to an angle are the two sides that meet at the angle. So ∠N is at N, meeting sides MN and LN. So the adjacent sides are MN (NM) and LN. The side opposite is ML. So the option "The side adjacent ∠N is $\overline{ML}$" is false because ML is opposite, not adjacent.

Wait, so correcting:

- True statements: "The side opposite ∠L is $\overline{NM}$", "The side opposite ∠N is $\overline{ML}$", "The hypotenuse is $\overline{LN}$".

Wait, earlier I thought "The side adjacent ∠L is $\overline{NM}$" was wrong, and "The side adjacent ∠N is $\overline{ML}$" was wrong. Let's confirm each option:

1. The side opposite ∠L is $\overline{NM}$: True (as explained).

2. The side opposite ∠N is $\overline{ML}$: True (side opposite ∠N is ML, since ∠N is at N, ML doesn't connect to N).

3. The hypotenuse is $\overline{NM}$: False (hypotenuse is LN).

4. The hypotenuse is $\overline{LN}$: True (opposite right angle at M).

5. The side adjacent ∠L is $\overline{NM}$: False (adjacent to ∠L are ML and LN; NM is opposite).

6. The side adjacent ∠N is $\overline{ML}$: False (adjacent to ∠N are MN and LN; ML is opposite).

So the true statements are: "The side opposite ∠L is $\overline{NM}$", "The side opposite ∠N is $\overline{ML}$", "The hypotenuse is $\overline{LN}$".

# Answer:
- The side opposite $\angle L$ is $\overline{NM}$ (True)
- The side opposite $\angle N$ is $\overline{ML}$ (True)
- The hypotenuse is $\overline{LN}$ (True)

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