State whether the following statements are true or false: (i) Every rectangle is a rhombus - Maths - Quadrilaterals

Question

State whether the following statements are true or false:

(i) Every rectangle is a rhombus
(ii) Every square is a rhombus

(iii) Every square is a rectangle
(iv) Every square is a parallelogram

(v) Every rectangle is a square
(vi) Every rectangle is a parallelogram

(vii) Every rhombus is a square
(viii) Every rhombus is a parallelogram

(ix) Every parallelogram is a rhombus

Ashutosh Verma · Accepted Answer

Dear Student,

Please find below the solution to the asked query:

( i ) Every rectangle is a rhombus False ( As
rectangle does not have all sides equal to each other as in rhombus
)

( ii ) Every square is a rhombus True ( Satisfied
all conditions )

( iii ) Every square is a rectangle False ( As
rectangle does not have all sides equal to each other as in square
)

( iv ) Every square is a parallelogram True (
Satisfied all conditions )

( v ) Every rectangle is a square False ( As
rectangle does not have all sides equal to each other as in square
)

( vi ) Every rectangle is a parallelogram True (
Satisfied all conditions )

( vii ) Every rhombus is a square False ( As that
is not necessarily all angles at 90° in rhombus as in square
)

( viii ) Every rhombus is a parallelogram True (
Satisfied all conditions )

( ix ) Every parallelogram is a rhombus False ( As
parallelogram does not have all sides equal to each other as in
rhombus )

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(i) Every rectangle is a rhombus.	(ii) Every square is a rhombus.
(iii) Every square is a rectangle.	(iv) Every square is a parallelogram.
(v) Every rectangle is a square.	(vi) Every rectangle is a parallelogram.
(vii) Every rhombus is a square.	(viii) Every rhombus is a parallelogram.
(ix) Every parallelogram is a rhombus.