n ΔMNO m∠O < m∠M < m∠N. List the side lengths in order from shortest to longest.
Responses
A NO, MN, MONO, MN, MO
B MO, NO, MNMO, NO, MN
C MN, NO, MOMN, NO, MO
D MN, MO, NOMN, MO, NO
C MN, NO, MOMN, NO, MO
why
In the given triangle nΔMNO, we know that m∠O < m∠M < m∠N.
Based on this, we can infer that side NO is the shortest, followed by side MN, and then side MO is the longest.
Therefore, the correct order of side lengths from shortest to longest is MN, NO, MO, and we also need to include the diagonal length MOMN (as it is typically longer than the other sides), which gives us the final order of: MN, NO, MOMN, NO, MO.
Thus, the correct answer is C) MN, NO, MOMN, NO, MO.
To determine the side lengths in order from shortest to longest, we can analyze the given information.
The given notation "n ΔMNO" implies that we have a triangle with vertices M, N, and O.
The notation "m∠O < m∠M < m∠N" indicates that the angle at O is the smallest, followed by the angle at M, and finally the angle at N.
Since the angles of a triangle are related to its sides, we can use this information to determine the order of the side lengths.
In a triangle, the longest side is always opposite the largest angle, the shortest side is opposite the smallest angle, and the remaining side falls in between.
Therefore, the correct answer is option D: MN, MO, NO.