Question

Which of the following statements is false? Select all that apply.

1- All trapezoids are parallelograms.
2- All parallelograms are trapezoids.
3- All squares are rectangles.
4- All rhombuses are rectangles.
5- All rectangles are squares.

Answer 1

The false statements are option (1),(4) and (5).

Explanation:

• Parallelograms and trapezoids are both types of quadrilaterals.

Parallelograms, which have two pairs of parallel sides, should be regarded as trapezoids. Others define a trapezoid as a quadrilateral with at least one pair of parallel sides (the inclusive definition), making the parallelogram a special type of trapezoid.

• So a square is a special kind of rectangle, it is one where all the sides have the same length. Thus every square is a rectangle because it is a quadrilateral with all four angles right angles. However not every rectangle is a square, to be a square its sides must have the same length.
• Rhombuses may be rectangles, as long as the shape is a square.

Hence from the above three statements we could clearly see that option (1),(4) and (5) are false statements.