Question

Which of the following statements are correct?

Statement 1: All rhombuses are not squares but all squares are rhombuses.
Statement 2: All rhombuses are squares but all squares are not rhombuses.
Statement 3: A parallelogram can be a rectangle or a square.
Statement 4: All squares are parallelograms but not all rectangles are parallelograms.

• A. Statements 1 and 3
• B. Statements 2 and 3
• C. Statements 3 and 4
• D. Statements 1 and 2

Answer 1

The correct option is A Statements 1 and 3


$\text{Statements 1 and 2:}$
For a shape to be called a rhombus, all of its sides must be of equal length.
As all squares have sides of equal length, every square is a rhombus. However, vice versa may not be true as not all rhombus have 90-degree angles.
Hence, statement 1 is correct while statement 2 is incorrect.

$\text{Statements 3 and 4:}$
For a shape to be called a rectangle, opposite sides should be parallel and equal to each other, and all angles should be right angles.

Similarly, for a shape to be called a square, all sides should be equal to each other, and all angles should be right angles.
So, when the above condition is satisfied, a parallelogram can be a rectangle or a square. Hence, statement 3 is correct.

Statement 4 $-$ not all the rectangles are parallelograms, is incorrect.

Therefore, option D is correct.