ANSWER TRUE OR FALSE a . all rectangles are square b. all rhombus are parallelogram c . all squares are rhombus and also rectangles d . all square are not parallelogram
The Correct Answer and Explanation is:
Let’s break down each statement:
a. All rectangles are squares — FALSE
While every square is a rectangle, the reverse is not true. A rectangle is defined as a quadrilateral with four right angles. However, a square has four right angles and all sides of equal length. Therefore, a rectangle with unequal side lengths cannot be a square. Hence, not all rectangles are squares.
b. All rhombuses are parallelograms — TRUE
A rhombus is a special type of parallelogram. It is defined as a quadrilateral where all four sides have equal length, and opposite sides are parallel. Since a parallelogram is defined by having opposite sides that are parallel, all rhombuses meet this criterion. Therefore, all rhombuses are parallelograms.
c. All squares are rhombuses and also rectangles — TRUE
A square is a special type of both rhombus and rectangle. A rhombus is defined by having all sides of equal length and opposite sides parallel, which a square satisfies. A rectangle is defined as having four right angles, and since a square has four right angles, it also satisfies the criteria for a rectangle. Therefore, every square is both a rhombus and a rectangle.
d. All squares are not parallelograms — FALSE
As mentioned earlier, a square is a special type of parallelogram. All squares have opposite sides that are parallel, and the opposite angles are equal. These are the key properties of a parallelogram, so all squares are indeed parallelograms.
In summary:
- a. False
- b. True
- c. True
- d. False
