Question

All squares are ______ but all _______ are not squares.
Which of the followings can fill the blank.

• A. Trapezoid
• B. Parallelogram
• C. Rhombus
• D. Rectangle

Answer 1

Answer: (B), (C), (D)

Rectangle

A square has all the sides equal in measure and all the interior angles equal in measure i.e. ${90}^o$.
All properties of a rectangle or a rhombus are satisfied in each square but all properties of a square does not satisfy in each rhombus or rectangle.

Hence, All squares are rectangle or rhombus but all rhombus or rectangles are not squares.

Similiarly, opposite sides of a square are parallel and equal. Opposite angles are equal.
That means all properties of a parallelogram are satisfied in each square but all properties of square does not satisfy in each parallelogram.

Hence, all squares are parallelograms but all prallelograms are not squares.

Trapezoid have one pair of non-parallel sides that is not possible in any square.
Hence, squares can not be trapezoid and vice-versa.

The following figure shows the combination of sets;