MATH SOLVE

4 months ago

Q:
# If quadrilateral PQRS is a rectangle, then which of the following is true? A. ∠PSQ ≅ ∠QSR B.segment SR ≅ segment RQ C.∠STP ≅ ∠QTR D.segment PS ≅ segment PR

Accepted Solution

A:

∠STP ≅ ∠QTR is the True statement ⇒ answer CStep-by-step explanation:In any rectangle1. Each two opposite sides are equal and parallel2. The measure of its vertex angles is 90°3. The two diagonals are equalNow lets find the true statements∵ PQRS is a rectangle∴ PS = QR ⇒ opposite sides∴ PQ = SR ⇒ opposite sides∴ PR = QS ⇒ diagonalsA. ∠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 ⇒ FalseB. 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 RQsegment SR ≅ segment RQ ⇒ FalseC. ∠STP ≅ ∠QTR∵ PR intersects QS at point T∴ m∠STP = m∠QTR ⇒ vertically opposite angles∴ ∠STP ≅ ∠QTR∠STP ≅ ∠QTR ⇒ TrueD. 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 PRsegment PS ≅ segment PR ⇒ False∠STP ≅ ∠QTR is the True statementLearn more:You can learn more about rectangle in brainly.com/question/6594923#LearnwithBrainly