Question

triangle inequalities
which statement is true regarding triangle tuv?
angles u and t must be equal.
angle t is the smallest angle.
angles u and v must be equal.
angle v is the smallest angle.

Explanation:

Step1: Recall the triangle - angle relationship

In a triangle, the larger the side length, the larger the angle opposite it.

Step2: Analyze the side - angle relationships in \(\triangle TUV\)

In \(\triangle TUV\), \(TU = 5\) units, \(UV=8\) units, and \(TV = 11\) units.
The angle opposite \(TU\) is \(\angle V\), the angle opposite \(UV\) is \(\angle T\), and the angle opposite \(TV\) is \(\angle U\).
Since \(TU\lt UV\lt TV\), by the triangle - angle relationship (the smaller the side, the smaller the angle opposite it), we have \(\angle V\lt\angle T\lt\angle U\)

Answer:

Angle \(V\) is the smallest angle.