Which of the following statements are true and which are false?

Question:

Which of the following statements are true and which are false?

(i) The diagonals of a parallelogram are equal.

(ii) The diagonals of a rectangle are perpendicular to each other.

(iii) The diagonals of a rhombus are equal.

(iv) Every rhombus is a kite.

(v) Every rectangle is a square.

(vi) Every square is a a parallelogram.

(vii) Every square is a rhombus.

(viii) Every rectangle is a parallelogram.

(ix) Every parallelogram is a rectangle.

(x) Every rhombus is a parallelogram.

Solution:

(i) The given statement is false.

The diagonals of a parallelogram bisect each other, but they are not equal in length.

(ii) The given statement is false.

The diagonals of a rectangle are equal and bisect each other, but they are not perpendicular.

(iii) The given statement is false.

All the sides of a rhombus are equal, but the diagonals are not equal.

(iv) The given statement is true.

(v) The given statement is false.

Every square is a rectangle, but every rectangle is not a square.

(vi) The given statement is true.

(vii) The given statement is true.

(viii) The given statement is true.

(ix) The given statement is false.

A rectangle is a special type of parallelogram, but every parallelogram is not a rectangle.

(x) The given statement is true.

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