Understanding shape

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Step 1: Check whether the curve cuts itself. Step 2: It does not cut itself. Answer: It is an open curve.

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Step 1: Check whether the curve cuts itself. Step 2: It cuts itself. Answer: It is a closed curve.

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Step 1: The curve is closed. Step 2: It does not pass through any point more than once. Answer: It is a simple closed curve.

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Step 1: In everyday use, curve means not straight. Step 2: In mathematics, the word curve is broader. Step 3: A straight line is also counted as a curve. Answer: A straight line is called a curve in m…

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Step 1: A closed curve divides the plane into parts. Step 2: The parts are interior, boundary, and exterior. Answer: It divides the plane into three parts: interior, boundary, and exterior.

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Step 1: A polygon needs its segments to intersect only at end-points. Step 2: Here the segments intersect at a point that is not an end-point. Answer: No, it is not a polygon.

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Step 1: In a polygon, each end-point must be shared by only two line segments. Step 2: Here one end-point is shared by three line segments. Answer: No, it is not a polygon.

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Step 1: A polygon must be a closed figure. Step 2: Each end-point must be shared by only two line segments. Step 3: Both conditions fail here. Answer: No, it is not a polygon.