Question

comparing side lengths name the shortest and longest sides of the triangle. 7.

Explanation:

Step1: Recall the triangle angle - side relationship

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

Step2: Identify the angles

The angles of the triangle are \( \angle S = 50^{\circ}\), \( \angle R=65^{\circ}\), \( \angle T = 65^{\circ}\).

Step3: Compare the angles

Since \( \angle S<\angle R=\angle T\).

Step4: Determine the sides opposite the angles

The side opposite \( \angle S\) is \( RT\), the side opposite \( \angle R\) is \( ST\), and the side opposite \( \angle T\) is \( SR\).

Answer:

The shortest side is \( RT\) and the longest sides are \( ST\) and \( SR\) (since \( \angle R=\angle T\), their opposite sides \( ST\) and \( SR\) are equal in length and longer than \( RT\)).