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Answer variants:
OQ=SP
Using CPCT
ΔPOQΔSOP
ΔPOQΔPSO
POQ+PSO=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
OP=OP
POQ=PSO
Opposite sides of a parallelogram are equal
POQ+SOP=180°
POQ=SOP
Show that the diagonals of a rhombus are perpendicular to each other.
 
A21.png
 
S. No.
Statement
Reason
1.
\(PQRS\) is a parallelogram.
Rhombus is also a parallelogram.
2.
OQ=OS
3.
Common side
4.
PQ=SP
5.
\(SSS\) Congruence rule
6.
CPCT
7.
Linear pair
8.
POQ=90°
 
Hence, the diagonals of a rhombus are perpendicular to each other.