In the diagram, |PQ| = |PS| Which of the following statements is true?
Attached Figure / Diagram
A
∠QPS = QRS
B
|PO| = |RO|
C
QR||PS
D
∠PQR=∠PSR
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
The given figure is a kite.
Here are the properties of a kite:
Two Pairs of Adjacent Sides: A kite has two pairs of adjacent sides that are equal in length.
Diagonals: The diagonals of a kite are perpendicular to each other. One diagonal bisects the other.
Symmetry: A kite has one line of symmetry, which runs along the longer diagonal.
Angles: The angles between the unequal sides are equal. Specifically, the angles opposite the equal sides are also equal.
Therefore, ∠PQR = ∠PSR is correct.
Source: WAEC / JAMB / NECO Classroom Archive (Record #26467)