Answer:
To determine the true statements regarding quadrilateral WXYZ, which is similar to quadrilateral QRST:
1. When two figures are similar, corresponding sides are in proportion. Let's denote the corresponding sides of quadrilateral QRST and WXYZ:
- QR corresponds to WX
- RS corresponds to XY
- ST corresponds to YZ
- TQ corresponds to ZW
2. Given that WX = 5 inches, we need to determine the lengths of the other sides based on the similarity ratio.
3. True statements:
A. WZ = 15/2 inches:
- This is true because if WX = 5 inches, and WZ corresponds to ST, which is three times the length of WX in quadrilateral QRST, then WZ = 3 * 5 = 15 inches. Therefore, WZ = 15/2 = 7.5 inches.
B. ZY = 25 inches:
- This statement is not necessarily true as the ratio of corresponding sides must be maintained in similar figures. Without additional information, we cannot determine this value based solely on the similarity.
C. The area of quadrilateral WXYZ is 525/8 square inches:
- To determine the area of a quadrilateral, we need more information than just the side lengths. Without the angles or additional measurements, we cannot accurately calculate the area. Hence, this statement cannot be verified without further details.
Therefore, the true statement is:
A. WZ = 15/2 inches.
Step-by-step explanation: