QQuestionMathematics
QuestionMathematics
Every quadrilateral is a rectangle.
True/False
Every square is a quadrilateral.
True/False
Every rectangle with four congruent sides is a square.
True/False
Every rhombus is a rectangle.
True/False
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Answer
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Step 1:I'll solve this problem step by step, addressing each statement carefully:
Step 2:: "Every quadrilateral is a rectangle" - False
- Definition: A quadrilateral is any four-sided polygon - A rectangle is a specific type of quadrilateral with four right angles - Not all quadrilaterals have right angles (e.g., trapezoids, kites) - Therefore, this statement is false
Step 3:: "Every square is a quadrilateral" - True
- Definition: A square is a four-sided polygon with:
Step 4:
Four equal sides
Step 5:
Four right angles - By definition, a square has four sides - Therefore, every square is indeed a quadrilateral
Step 6:: "Every rectangle with four congruent sides is a square" - True
- A rectangle with four congruent sides meets the definition of a square - Conditions for a square:
Step 7:
Four equal sides ✓
Step 8:
Four right angles ✓ - Therefore, this statement is true
Step 9:: "Every rhombus is a rectangle" - False
- A rhombus has four equal sides but not necessarily right angles - A rectangle requires right angles - Therefore, not every rhombus is a rectangle
Final Answer
1. False 2. True 3. True 4. False
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