Question

given the information marked on each figure below, select all classifications that must be true
note that each figure is drawn like a rectangle, but you should not rely on the way the figure is drawn in determining your answers.
if necessary, you may learn what the markings on a figure indicate.

Explanation:

Figure 1

• Quadrilateral: A quadrilateral is a four - sided polygon. Since \(RSTU\) has four sides, it is a quadrilateral.
• Parallelogram: In a parallelogram, the diagonals bisect each other. In \(RSTU\), the diagonals \(RT\) and \(SU\) bisect each other (marked as equal segments), so \(RSTU\) is a parallelogram.
• Rectangle: For a parallelogram to be a rectangle, the diagonals must be equal. There is no information given about the equality of the diagonals of \(RSTU\) (only that they bisect each other), so we cannot conclude it is a rectangle.

Figure 2

• Quadrilateral: \(ABCD\) has four sides, so it is a quadrilateral.
• Parallelogram: A quadrilateral with four right angles. A quadrilateral with four right angles is a rectangle. A rectangle is a type of parallelogram (a parallelogram with four right angles).
• Rectangle: Since \(ABCD\) has four right angles (marked as right - angle symbols), it is a rectangle.

Figure 3

• Quadrilateral: \(WXTV\) has four sides, so it is a quadrilateral.
• Parallelogram: A quadrilateral with one pair of opposite sides parallel and equal (marked as equal segments) and one right angle. A quadrilateral with one pair of opposite sides parallel and equal is a parallelogram. A parallelogram with one right angle has four right angles (because in a parallelogram, consecutive angles are supplementary. If one angle is \(90^{\circ}\), then all angles are \(90^{\circ}\)).
• Rectangle: A parallelogram with four right angles is a rectangle.

Answer:

• For the first figure: Quadrilateral, Parallelogram
• For the second figure: Quadrilateral, Parallelogram, Rectangle
• For the third figure: Quadrilateral, Parallelogram, Rectangle