Question 1: A square is a rhombus but a rhombus is not a square.
This statement is wholly justified. A rhombus is a figure which has 4 lines of equal length and whose top is parallel to the bottom and whose side is parallel to its opposite. A square is a figure that has 4 lines of equal length, whose top is parallel to the bottom and whose side is parallel to its opposite. A square also has 4 angles of which all equal 90 degrees.
Thus, since a square fulfills all the requirements of being a rhombus, a square is also a rhombus but since a rhombus does not fulfill all the requirements of being a square, not all rhombi are squares.
The answer is (D) and my justification is shown below:
Quadrilaterals are figures which have 4 sides, angles and vertices. A square has 4 angles, sides and vertices. A parallelogram is a figure that has 4 sides, 4 angles and 4 vertices. Thus, squares and parallelograms are quadrilaterals.
A square has 2 pairs of parallel lines, top-bottom and side-side. A parallelogram has 2 pairs of parallel lines, to-bottom and side-side. Thus, opposite sides of squares and parallelograms are parallel.
A trapezoid is a figure with 1 pair of parallel lines and 1 pair of non-parallel lines.
All parallelograms are squares.
I do not agree with this statement. Squares are figures with 4 sides, 4 angles that are 90º each and 2 pairs of parallel lines. Parallelograms have 4 sides, 4 angles that do not need to be 90º each and 2 pairs of parallel lines. Thus, this statement is false.