True or False? True Every rhombus is a rectangle. False True Every square is a parallelogram. False True Every quadrilateral is a rhombus. False True Every rhombus with four right angles is a square. False
The Correct Answer and Explanation is :
Here are the correct answers and explanations for each statement:
1. Every rhombus is a rectangle.
Answer: False
A rhombus is a quadrilateral where all sides are equal in length, but its angles are not necessarily 90 degrees. A rectangle requires all angles to be 90 degrees, which is not true for every rhombus. Only rhombuses with right angles are also rectangles, which makes this statement false.
2. Every square is a parallelogram.
Answer: True
A square is a specific type of parallelogram because it has two pairs of parallel sides, opposite sides are equal in length, and opposite angles are equal. Since a square fulfills all the criteria of a parallelogram, this statement is true.
3. Every quadrilateral is a rhombus.
Answer: False
A quadrilateral is any four-sided polygon, which includes shapes like rectangles, trapezoids, and kites, among others. A rhombus is a specific type of quadrilateral where all four sides are equal. Since not all quadrilaterals meet this condition, this statement is false.
4. Every rhombus with four right angles is a square.
Answer: True
If a rhombus has four right angles, it meets the criteria for a square. A square is a rhombus with all sides equal and all angles equal to 90 degrees. Therefore, this statement is true.
Explanation (300 words):
A rhombus is a quadrilateral with all sides equal but does not necessarily have right angles. A rectangle has opposite sides equal and all angles 90 degrees. While a square is both a rhombus and a rectangle, not all rhombuses qualify as rectangles because they may lack right angles.
A parallelogram is a quadrilateral with opposite sides parallel and equal. Since a square meets these criteria, every square is a parallelogram.
A quadrilateral is a broad category that includes any four-sided polygon. Not all quadrilaterals are rhombuses because most quadrilaterals (e.g., trapezoids and kites) do not have all sides equal in length.
Finally, a rhombus with four right angles must also meet the criteria for a square: equal sides and right angles. Hence, the rhombus in this case is also a square.