QQuestionMathematics
QuestionMathematics
"Is a trapezoid always a quadrilateral?
A. Yes
B. No"
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:I'll solve this problem step by step:
Step 2:: Understand the definitions
- A quadrilateral is a polygon with exactly 4 sides - A trapezoid is a quadrilateral with at least one pair of parallel sides
Step 3:: Analyze the definition of a trapezoid
- By definition, a trapezoid has 4 sides - This means a trapezoid MUST be a quadrilateral - The parallel sides requirement is an additional characteristic of trapezoids
Step 4:: Logical reasoning
- Since a trapezoid is defined as having 4 sides, it automatically meets the definition of a quadrilateral - All trapezoids are, by definition, quadrilaterals - Not all quadrilaterals are trapezoids, but all trapezoids are quadrilaterals
Step 5:: Conclusion
- The statement "A trapezoid is always a quadrilateral" is TRUE
Final Answer
Yes, a trapezoid is always a quadrilateral. Key Insight: The definition of a trapezoid inherently includes having 4 sides, which is the defining characteristic of a quadrilateral.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students