State whether True or False and justify your answer. All rectangles are squares. All rhombus are parallelogram All square are rhombus. please explain this
The Correct Answer and Explanation is:
Let’s go through each statement one by one:
- All rectangles are squares
False. A rectangle is a quadrilateral with four right angles, but its sides do not have to be of equal length. A square, on the other hand, is a special type of rectangle where all four sides are equal in length. Therefore, while all squares are rectangles, not all rectangles are squares. A rectangle can have unequal adjacent sides, making it different from a square. - All rhombuses are parallelograms
True. A rhombus is a type of parallelogram where all four sides are of equal length. Parallelograms, by definition, are quadrilaterals where opposite sides are parallel and equal in length. Since a rhombus satisfies the conditions of a parallelogram (opposite sides are parallel and equal), it is indeed a parallelogram. The additional property of equal sides makes it a rhombus, but this does not disqualify it from being a parallelogram. - All squares are rhombuses
True. A square is a quadrilateral with all four sides equal in length and all four angles being right angles. A rhombus is defined as a quadrilateral where all four sides are equal in length, but the angles are not necessarily 90 degrees. Since a square has equal-length sides (a requirement for a rhombus) and is a special case of a rhombus with right angles, every square is a rhombus. Therefore, the statement is true.
In summary, the truth values of the statements are:
- All rectangles are squares: False.
- All rhombuses are parallelograms: True.
- All squares are rhombuses: True.
