The length of NM line segment for the considered situation is given by: Option D: 50 mi
What are congruent triangles?
Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF\\[/tex]
(|AB| denotes length of line segment AB, and so on for others).
For these cases, the two triangles in the image are congruent.
So their corresponding sides must be of same measures.
The three sides of triangle RST are of measures 75, 67 and 50 miles
The two sides of triangle NLM are 67 miles and 75 miles. So obviously third one can be nothing except 50 miles so that the triangle NLM also have sides of same measure as of the triangle RST.
Thus, the length of NM line segment for the considered situation is given by: Option D: 50 mi
Learn more about congruent triangles here:
https://brainly.com/question/16921692
