We can see here that:
- The polygon QRST meets the criteria for being a parallelogram.
- It also meets the criteria for being a rhombus due to its equal side lengths.
Based on the given information, we can determine the properties of the polygon QRST.
1. QR | ST: This notation indicates that QR is parallel to ST. Therefore, opposite sides QR and ST are parallel.
2. RS || TQ: This notation indicates that RS is parallel to TQ. Therefore, opposite sides RS and TQ are parallel.
From the given information, we can conclude that QRST is a parallelogram.
Now, let's analyze the lengths of the sides:
Since all sides of QRST are congruent, we can conclude that QRST is a rhombus.
However, we need to consider the angles to further determine the type of rhombus.
- ∠Q = ∠S = 90°: A rhombus with right angles is called a rectangle.
- ∠Q ≠ ∠S: If the angles are not right angles, we can conclude that QRST is not a rectangle.
Therefore, based on the given information, we can conclude that QRST is a rhombus, but it is not a rectangle or a square.
To summarize, the correct answers are: