Question

Which of the following is a TRUE statement?

• A. All rectangles are parallelograms
• B. All rectangles are squares
• C. All rectangles are Rhombuses
• D. All squares are not parallelograms

Hint:

Hierarchy of Quadrilaterals: - Parallelogram (opposite sides parallel) - Rectangle (parallelogram with right angles) - Square (rectangle with equal sides) - Rhombus (parallelogram with equal sides) - Square (rhombus with right angles) A square is a special type of rectangle, rhombus, and parallelogram. A rectangle is a special type of parallelogram. A rhombus is a special type of parallelogram.

Answer 1

The Correct Option is A

Step 1: Define the properties of the geometric shapes involved.
- Parallelogram: A quadrilateral with two pairs of parallel sides.
Opposite sides are equal in length, and opposite angles are equal.
- Rectangle: A parallelogram with all four angles being right angles (90 degrees).
- Square: A rectangle with all four sides equal in length.
(Alternatively, a rhombus with all right angles).
- Rhombus: A parallelogram with all four sides equal in length.
Opposite angles are equal, and diagonals bisect each other at right angles.

Step 2: Evaluate each statement.
Option (1) All rectangles are parallelograms: A rectangle has two pairs of parallel sides (by definition, as it's a special type of parallelogram).
This statement is TRUE.
Option (2) All rectangles are squares: A square is a rectangle where all sides are equal.
A rectangle can have unequal adjacent sides (e.
g.
, length = 5, width = 3).
So, not all rectangles are squares.
This statement is FALSE.
Option (3) All rectangles are Rhombuses: A rhombus has all four sides equal.
A rectangle can have unequal adjacent sides.
So, not all rectangles are rhombuses (unless it's a square, which is both).
This statement is FALSE.
Option (4) All squares are not parallelograms: A square has two pairs of parallel sides (as it's a special rectangle, which is a special parallelogram).
So, all squares are parallelograms.
This statement is FALSE.

Step 3: Identify the true statement.
The only true statement is "All rectangles are parallelograms.
" This matches option (1).