Question

rectangle pqrs is shown with its diagonals, (overline{pr}) and qs. what type of triangle is (\triangle str)? right triangle equilateral triangle isosceles triangle scalene triangle

Explanation:

Step1: Properties of rectangle diagonals

In a rectangle, the diagonals are equal and bisect each other. So \(PR = QS\), and \(ST=\frac{1}{2}QS\), \(RT = \frac{1}{2}PR\). Since \(PR = QS\), we have \(ST=RT\).

Step2: Definition of triangle types

• A right - triangle has one \(90^{\circ}\) angle. There is no information given about a \(90^{\circ}\) angle in \(\triangle STR\).
• An equilateral triangle has all sides equal. We only know \(ST = RT\), not that \(SR=ST = RT\).
• An isosceles triangle has at least two sides equal. Since \(ST = RT\), \(\triangle STR\) satisfies this.
• A scalene triangle has all sides of different lengths. But \(ST = RT\), so it is not scalene.

Answer:

isosceles triangle