Consider the following statement and decide whether it is true or false.All rhombuses are squares.Answer:The statement is .
Question
Consider the following statement and decide whether it is true or false.
All rhombuses are squares.
Answer: The statement is .
Solution
Analysis of the Statement
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Understanding Rhombuses and Squares: A rhombus is defined as a quadrilateral with all four sides of equal length. A square, on the other hand, is a special type of rhombus that also has all angles equal to 90 degrees.
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Consideration of Properties: Since all squares are rhombuses (because they satisfy the condition of having equal sides), it does not mean all rhombuses are squares. A rhombus can have angles that are not right angles, which disqualifies it from being a square.
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Counterexamples: A rhombus with angles of 60 degrees and 120 degrees illustrates that while it is a rhombus, it is not a square.
Conclusion
The statement "All rhombuses are squares" is false.
Final Answer
The statement is false.
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