Q1) I agree with this statement as a square has all the properties of a rhombus. It has four equal sides, the opposites sides are parallel, the diagonals are perpendicular to each other, opposite angles are equal and all interior angles add up to 360˚. This qualifies a square to be a rhombus. But a rhombus does not have one vital property that qualifies it to be a square. A rhombus does not have all interior angles to be 90˚. This immediately shows that a rhombus cannot be a square making the statement ‘A square is a rhombus but a rhombus is not a square’ correct.

Q4) I totally disagree with this statement. A parallelogram can never be a square. They do share some properties like all sides being parallel and opposite angles being the same but they have many differences that eliminates the possibility of them being the same. For example a square has equal sides but the parallelogram only has opposite sides being equal and a square has 90˚ angles but a parallelogram only has opposite angles being equal. These very significant property difference proves this entire statement to be wrong.

Q5) I agree to the statemnt for a two reasons. First reason being the picture itself. It definitely shows that that is a parallelogram. The second reason being BF & ED are the same length. This shows that no matter how far apart these two lines is they will always be the same length which automatically makes it a parallelogram unless BF or ED is rotated.

Good observations Shakti -it shows deep thinking

ReplyDeleten fair amount of reading. Checkout the term 'subset' examples equilateral triangle us a subset of triangles and apply it to your solution. This will further strengthen your claim.