Question

State whether the following statements are true or false. Also, justify your answer in each case.

1. All rectangles are Squares
2. All Squares are trapeziums
3. All rhombuses are parallelograms

Answer 1

2 and 3 are true here, but 1 is not true.

Here, All rectangles are not squares. If a rectangle has length = 6 cm and breadth = 3 cm, then it is not a square because a Square should have all its sides equal

All Squares are trapeziums, because All Squares have at least one pair of opposite sides which are parallel.

All Rhombuses are parallelograms, because all rhombuses have opposite sides equal and parallel, opposite angles equal, and adjacent angles supplementary. Also, just like parallelograms, the diagonals of a rhombus bisect each other and divide it into 2 congruent triangles.