State whether the statements are true (T) or false (F).

Diagonals of a rhombus are equal and perpendicular to each other.

FALSE

Consider rhombus ABCD,

You know that , AB=BC=CD=AD

Now , in ΔAED and ΔCED,

EA = EC (diagonals of a parallelogram bisect each other)

ED= ED (common)

AD=CD

⸫ ΔAED is congruent to ΔCED (SSS)

This gives that AED = CED (CPCT)

But, AED + CED = 180° (linear pair)

So , 2 × AED = 180°

⸫AED = 90°

So , the diagonals of rhombus are only perpendicular to each other.

⸫ the diagonals of rhombus are perpendicular but not equal.