Rhombus - Rectangle - Square

[kannn]

Q-I) Is quadrilateral ABCD a rectangle?

 

(1) Line segments AC and BD bisect one another.

 

(2) Angle ABC is a right angle.

 

 

C

 

 

Q-II) Is quadrilateral ABCD a rhombus?

 

(1) Line segments AC and BD are perpendicular bisectors of each other.

 

(2) AB = BC = CD = AD

 

 

D

 

 

I didnt quite get the answers initially. But later understood it.

Does all the Squares can be considered as Rectangle??? [Ans behind Q1]

Does all the Squares can be considered as Rhombus??? [Ans behind Q2]

 

I think there is some kind of subset kind of relationship between Rectangle - Square - Rhombus and Parallelogram. Can someone list it out please?

 

Please explain your answers.

Thanks guys.

[ken_english]

for Q2, shouldn't a rhombus have all sides equal ?

[givemeanid]

All squares are rhombus. Inverse is not true.

All squares are rectangles. Inverse is not true.

 

Squares, rhombuses and rectangles are parallelograms.

[kannn]

Thank you so much givemeanid.Sply for the 3rd one.

[shool]

I differ on this point: all squares are rectangles. squares are NOT a special case of rectangles. In a rectangle opposite sides need to be equal but in a square all sides have to be equal. This does not mean that a square is subset of rectangle.

Yes square is a special case of a rhombus becoz:

Rhombus: all sides are equal and diagonals are equal and bisect each other

Square: all sides are equal and 90degrees and diagonals are equal and bisect each other.

So a square is a special case of rhombus.

[kannn]

"In a rectangle opposite sides need to be equal but in a square all sides have to be equal."

 

shool, of course in square opposite sides are equal (not only opposite sides, but also all the sides). So it is rectangle. But vice-versa is not true.