Question

The figure of the square □PQRS is given below. If the length of the diagonal PR is 6 cm, then answer the following questions.



(1) What is the length of the diagonal QS?
(2) l (QO) = ?
(3) l (PO) = ?
(4) m∠POS = ?

Answer 1

Given, l (PR) = 6 cm
(1) Diagonals of a square are congruent.
∴ l (QS) = l (PR) = 6 cm

(2) l (QO) = ?
Diagonals of a square bisect each other.
∴ l (QO) = l (OS) = $\frac{1}{2}\times l\left(\mathrm{QS}\right)$
∴ l (QO) = $\frac{1}{2}\times 6$ = 3 cm

(3) l (PO) = ?
Diagonals of a square bisect each other.
∴ l (PO) = l (OR) = $\frac{1}{2}\times l\left(\mathrm{PR}\right)$
∴ l (PO) = $\frac{1}{2}\times 6$ = 3 cm

(4) m∠POS = ?
Diagonals of a square bisect each other at right angles.
∴ m∠POS = 90°