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Question

Which of the following are true?

i) All squares are rhombuses.

ii) All parallelograms are rectangles.

iii) All rhombuses are kites.

iv) All squares are rectangles.


A

ii, iii

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B

i, ii

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C

i, iii, iv

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D

None of these

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Solution

The correct option is C

i, iii, iv


Rhombus has equal sides and their diagonals bisect each other at 90. Square also satisfies these conditions. So, (i) is true.

A rectangle has all angles equal to 90 This is not the case with parallelograms. So, (ii) is false.

A kite has two pairs of equal adjacent sides, one diagonal bisecting other and one pair of equal interior opposite angles. Rhombus satisfies all of these conditions. So, (iii) is true.

Rectangle has all angles as 90and equal opposite sides. Square also has all angles as 90 and all equal sides, hence equal opposite sides. So, (iv) is true.


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