Drag the correct answers — task. Mathematics CBSE, Class 9.

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Answer variants:

O Q = S P

Using CPCT

Δ P O Q ≅ Δ S O P

Δ P O Q ≅ Δ P S O

∠ P O Q + ∠ P S O = 180 °

All the sides of a parallelogram are equal

Diagonals of a parallelogram bisect each other

All the sides of a rhombus are equal

Using parallelogram property

O P = O P

∠ P O Q = ∠ P S O

Opposite sides of a parallelogram are equal

∠ P O Q + ∠ S O P = 180 °

∠ P O Q = ∠ S O P

Show that the diagonals of a rhombus are perpendicular to each other.

S. No.	Statement	Reason
1.	$PQRS$ is a parallelogram.	Rhombus is also a parallelogram.
2.	$O Q = O S$
3.		Common side
4.	$P Q = S P$
5.		$SSS$ Congruence rule
6.		CPCT
7.		Linear pair
8.	$∠ P O Q = 90 °$

Hence, the diagonals of a rhombus are perpendicular to each other.

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