Answer :
To determine whether the statement "If a quadrilateral is a rhombus and a rectangle, it is also a square" is true or false, let's analyze the properties of these shapes step-by-step:
1. Rhombus:
- A rhombus is a type of quadrilateral where all four sides have equal length.
- The angles are not necessarily 90 degrees, but the opposite angles are equal.
2. Rectangle:
- A rectangle is a type of quadrilateral where each of the interior angles is 90 degrees.
- The opposite sides are equal in length.
3. Square:
- A square is a type of quadrilateral that has all the properties of both a rhombus and a rectangle:
- All four sides are equal in length (like a rhombus).
- All four angles are 90 degrees (like a rectangle).
Now, given the definitions:
- If a quadrilateral is a rhombus, all sides are equal.
- If the same quadrilateral is also a rectangle, all angles are 90 degrees.
Since a quadrilateral with all sides equal and all angles equal to 90 degrees fits the definition of a square, we can conclude that:
True: If a quadrilateral is a rhombus and also a rectangle, it must also be a square.
Based on this analysis, the correct answer is:
A. True
1. Rhombus:
- A rhombus is a type of quadrilateral where all four sides have equal length.
- The angles are not necessarily 90 degrees, but the opposite angles are equal.
2. Rectangle:
- A rectangle is a type of quadrilateral where each of the interior angles is 90 degrees.
- The opposite sides are equal in length.
3. Square:
- A square is a type of quadrilateral that has all the properties of both a rhombus and a rectangle:
- All four sides are equal in length (like a rhombus).
- All four angles are 90 degrees (like a rectangle).
Now, given the definitions:
- If a quadrilateral is a rhombus, all sides are equal.
- If the same quadrilateral is also a rectangle, all angles are 90 degrees.
Since a quadrilateral with all sides equal and all angles equal to 90 degrees fits the definition of a square, we can conclude that:
True: If a quadrilateral is a rhombus and also a rectangle, it must also be a square.
Based on this analysis, the correct answer is:
A. True
