Which statements are true for triangle lnm? check all that apply. the side opposite ∠l is nm. the side opposite ∠n is ml. the hypotenuse is nm. the hypotenuse is ln. the side adjacent ∠l is nm. the side adjacent ∠n is ml.
The Correct Answer and Explanation is:
To answer these questions accurately, we’ll assume that triangle ( \triangle LNM ) is a right triangle, as terms like “hypotenuse” are typically used for right triangles. Let’s clarify each statement based on the properties of right triangles:
- The side opposite ( \angle L ) is ( NM ):
In any triangle, the side opposite an angle is the side that does not touch that angle. Here, ( NM ) does indeed oppose ( \angle L ), meaning it is the side opposite ( \angle L ).
- This statement is true.
- The side opposite ( \angle N ) is ( ML ):
Similarly, the side opposite ( \angle N ) would not touch ( \angle N ). Here, ( ML ) is indeed opposite ( \angle N ).
- This statement is true.
- The hypotenuse is ( NM ):
The hypotenuse is the longest side of a right triangle, located opposite the right angle. We are not told directly which angle is the right angle, but if we assume ( \angle M ) is the right angle, then the hypotenuse would be ( LN ), not ( NM ).
- This statement is false.
- The hypotenuse is ( LN ):
Assuming ( \angle M ) is the right angle, the hypotenuse would indeed be ( LN ), which is opposite the right angle.
- This statement is true.
- The side adjacent to ( \angle L ) is ( NM ):
In a right triangle, each acute angle has one adjacent side (besides the hypotenuse) that helps form that angle. If ( \angle M ) is the right angle, then ( NM ) is adjacent to both ( \angle L ) and ( \angle M ), making this statement true.
- This statement is true.
- The side adjacent to ( \angle N ) is ( ML ):
The side ( ML ) is adjacent to both ( \angle N ) and ( \angle M ) if ( \angle M ) is the right angle. Therefore, this is true as well.
- This statement is true.
Summary:
The true statements for triangle ( \triangle LNM ) are:
- The side opposite ( \angle L ) is ( NM ).
- The side opposite ( \angle N ) is ( ML ).
- The hypotenuse is ( LN ).
- The side adjacent to ( \angle L ) is ( NM ).
- The side adjacent to ( \angle N ) is ( ML ).