State whether True or False: All squares are rhombuses and also rectangles A. True B. False C. Ambiguous D. Data insufficient
Hint: First look at definitions of those 3 geometrical shapes. Now by using, decide the truthfulness of the given statement. Try to find interrelations between the three definitions. From that relation, find whether the first part of the statement is true or not. Similarly repeat this for the second part. Even if one of them is false the whole statement will be written false. This is the required result.
Complete step-by-step answer: Square: In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle in which 2 adjacent sides have equal lengths. It is a two-dimensional shape. Rectangle: In Euclidean plane geometry, a rectangle is a quadrilateral with 4 right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal. It can also be defined as a parallelogram containing a right angle. It is a two-dimensional shape. Rhombus: In Euclidean plane geometry, a rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, this name is analogy to equilateral triangle, as equilateral means that all of its sides are equal in length. Given statement in the question can be written as: All squares are rhombuses and also rectangles. First part of the statement can be written as: All squares are rhombuses. Explanation of the above statement is given in the way of: The basic condition of rhombus is that all sides are equal. This is satisfied by square. By above statement we can say that the statement: All squares are rhombuses is true. Second part of original statement can be written as: All squares are rectangles. Explanation of above statement is given in the way of: The basic condition of the rectangle is all angles being $90^0$. This is satisfied by square. Moreover in the definition of square we wrote it can be defined as a special type of rectangle. From above statement, we can say the statement: All squares are rectangles is true. As both are true the whole statement is true. Therefore, option (a) is correct.
Note: Be careful while stating the definitions. You must not miss the base point of their definition. Students confuse between statements and it’s vice versa. For example they confuse and solve all the squares are rhombuses as all rectangles are squares which may go wrong sometimes, so, read and solve the statement with at most care.
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