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In the diagram, |PQ| = |PS| Which of the following statements is true?

Mathematics
WAEC 2000

In the diagram, |PQ| = |PS| Which of the following statements is true?

  • A. ∠QPS = QRS
  • B. |PO| = |RO|
  • C. QR||PS
  • D. ∠PQR=∠PSR
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Correct Answer: Option D
Explanation

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.


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