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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.

Mathematics
RS Aggarwal (2016)
Standard VIII

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