Learn about 2-Dimensional Figures and Polygons 2-Dimensional Figures and Polygons. In this problem, it says to tell whether each figure is open or closed and is it a polygon. Before we begin, let’s talk about what a 2-dimensional figure is. A 2-dimensional figure is a shape with length and width. Now, 2-dimensional figure can either be an open figure or it can be a closed figure. A closed figure start and end at the same endpoint. An open figure does not start and end at the same endpoint. So, a 2-dimensional figure is a shape that has length and width and it could either be an open figure or it can be a closed figure. A closed figure starts and ends at the same point. In open figures, it does not start and end at the same point. Let’s talk about polygons for a second. Polygons are closed 2-dimensional figures that have three or more straight sides. The sides do not cross. One other thing to talk about are vertices; plural form of vertex. A vertex or vertices are the endpoints where two sides meet. Let’s take a look at figure A. Figure A does not start or end at the same endpoint and the line is curved. Remember that figures that do not start at the same endpoint are called open figures. So, Figure A is an open figure. Remember again that polygons are closed 2-dimensional figures which are entirely made of three or more straight sides. That means Figure A has curved sides. That means that Figure A is not a polygon. Let’s take a look at B. Figure B starts and ends at the same endpoint and remember that a closed figure starts and ends at the same endpoint. Therefore, Figure B is a closed figure. Figure B also is curved, so you noticed the lines are curved and remember, in order for a figure to be a polygon, it must be a closed 2-dimensional figure that have three or more straight sides. So, it has to be made up of straight sides. Therefore, Figure B is not a polygon. Let’s take a look at Figure C. Figure C starts and ends at the same endpoint. There are three line segments and a curved side which is not a line segment. Remember that figures that begin and end at the same point are closed figures, so this is a closed figure. A polygon must be closed figure which is made entirely of three or more straight line segments. Remember the keyword, is it has to be made up of straight line segments. Since there is a curved line in this figure, this figure is not a polygon. Let’s move on to number 2. Figure A for number 2 has two line segments but the ends do not meet. Remember that figures that have ends that do not meet are open figures, so A is an open figure. A polygon must be a closed figure which is made entirely of three or more straight line segments. Therefore, since this is an open figure, it is not a polygon. Let’s take a look at B. Figure B starts and ends at the same endpoint and there are six straight line segments. Remember that figures that begin and end at the same endpoint are closed figures, so B is a closed figure. Remember also that a polygon must be a closed figure which is entirely made up of three or more straight lines. Since this is made up of six straight lines, this is a polygon. This shape is a polygon. Let’s take a look at C. Now, Figure C starts and ends at the same endpoint and there are six straight line segments and the sides cross, right here they cross. Remember that figures that begin and end at the same points are closed figures, so C is a closed figure. Remember that a polygon must be a closed figure which is entirely made of three or more straight lines and the line segments, they do not cross. Since these cross, this is not a polygon. Things to remember and to keep in mind that a 2-dimensional figure is a shape with a length and a width and can either be open or closed. Open figures have ends that do not meet, so the ends do not have a start and endpoint. They don’t start and end at the same point. A closed figure, the figure begins and ends at the same point. Remember that polygons are closed 2-dim