In the diagram, |PQ| = |PS| Which of the following statements is true?
Answer Details
Since |PQ| = |PS|, we know that triangle PQS is an isosceles triangle. Therefore, the angles opposite the equal sides are equal, which means that ?QPS = ?PSQ.
Now, let's look at the answer choices:
?QPS = QRS: We cannot determine this from the information given. We do not know anything about the angle QRS.
|PO| = |RO|: We cannot determine this from the information given. We do not have any information about points P, O, and R.
QR||PS: We cannot determine this from the information given. We do not have any information about whether QR and PS are parallel or not.
?PQR = ?PSR: Since |PQ| = |PS|, we know that triangle PQS is an isosceles triangle. Therefore, ?PQS = ?PSQ. Also, since |PQ| = |PS| and PQRS is a parallelogram, we know that |QR| = |PS|. Therefore, triangle PSR is also an isosceles triangle, and ?SPR = ?PSR. Finally, since PQRS is a parallelogram, we know that ?PQR = ?SPR. Therefore, ?PQR = ?PSR.
