QQuestionMathematics
QuestionMathematics
TRUE OR FALSE: Every quadrilateral is a rhombus.
TRUE OR FALSE: Every rhombus is a quadrilateral.
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Step 1:I'll solve this step by step, carefully following the LaTeX formatting guidelines:
Step 2:: Understand the definitions
- A quadrilateral is a four-sided polygon with four vertices and four angles - A rhombus is a quadrilateral with four equal sides
Step 3:: Analyze the first statement "Every quadrilateral is a rhombus"
- This statement means ALL quadrilaterals must have four equal sides - Counterexample: A rectangle is a quadrilateral but not a rhombus - Therefore, this statement is FALSE
Step 4:: Analyze the second statement "Every rhombus is a quadrilateral"
- A rhombus, by definition, has four sides and four vertices - This means a rhombus MUST be a quadrilateral - Therefore, this statement is TRUE
Final Answer
- First statement (Every quadrilateral is a rhombus): \boxed{\text{FALSE}} - Second statement (Every rhombus is a quadrilateral): \boxed{\text{TRUE}} Key Insight: Not all quadrilaterals have equal sides, but all rhombuses are four-sided polygons (quadrilaterals).
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