∠STP ≅ ∠QTR is the True statement ⇒ answer C
Step-by-step explanation:
In any rectangle
1. Each two opposite sides are equal and parallel
2. The measure of its vertex angles is 90°
3. The two diagonals are equal
Now lets find the true statements
∵ PQRS is a rectangle
∴ PS = QR ⇒ opposite sides
∴ PQ = SR ⇒ opposite sides
∴ PR = QS ⇒ diagonals
A. ∠PSQ ≅ ∠QSR
∵ The diagonals of the rectangle do not bisect the vertex angles
∴ AQ does not bisect angle S
∴ m∠PSQ ≠ m∠QSR
∴ ∠PSQ not congruent ∠QSR
∠PSQ ≅ ∠QSR ⇒ False
B. segment SR ≅ segment RQ
∵ SR and RQ are two adjacent sides
∵ The adjacent side in the rectangle not equal
∴ SR ≠ QR
∴ segment SR not congruent to segment RQ
segment SR ≅ segment RQ ⇒ False
C. ∠STP ≅ ∠QTR
∵ PR intersects QS at point T
∴ m∠STP = m∠QTR ⇒ vertically opposite angles
∴ ∠STP ≅ ∠QTR
∠STP ≅ ∠QTR ⇒ True
D. segment PS ≅ segment PR
∵ PS is a side in the rectangle
∵ PR is a diagonal in the rectangle
∵ The side of the rectangle not equal the diagonal of the rectangle
∴ PS ≠ PR
∴ segment PS not congruent to segment PR
segment PS ≅ segment PR ⇒ False
∠STP ≅ ∠QTR is the True statement
Learn more:
You can learn more about rectangle in brainly.com/question/6594923
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