QQuestionMathematics
QuestionMathematics
"True or False?
Every square is a rectangle.
Every rhombus is a quadrilateral.
Every rhombus with four right angles is a square.
Every quadrilateral is a rectangle."
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Answer
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Step 1:I'll solve this problem by carefully analyzing each statement and providing a clear, step-by-step explanation.
Step 2:: Understand the Definitions
- Rectangle: A quadrilateral with four right angles - Square: A rectangle with all sides equal in length - Rhombus: A quadrilateral with four equal sides - Quadrilateral: A polygon with four sides
Step 3:: Analyze First Statement - "Every square is a rectangle"
- A square has four right angles ✓ - A square has equal side lengths ✓ - By definition, a square meets all rectangle requirements - Therefore, this statement is TRUE
Step 4:: Analyze Second Statement - "Every rhombus is a quadrilateral"
- A rhombus has four sides ✓ - A quadrilateral is defined as a polygon with four sides ✓ - Therefore, this statement is TRUE
Step 5:: Analyze Third Statement - "Every rhombus with four right angles is a square"
- A rhombus with four right angles means:
Step 6:
All sides are equal
Step 7:
All angles are 90 degrees - This precisely defines a square - Therefore, this statement is TRUE
Step 8:: Analyze Fourth Statement - "Every quadrilateral is a rectangle"
- A quadrilateral can have: - Varying side lengths - Varying angle measurements - Not all quadrilaterals have right angles - Therefore, this statement is FALSE
Final Answer
1. True 2. True 3. True 4. False
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