Video: Dividing a Given Polygon into Two Polygons with the Same Number of Sides

Video Transcript

I want to join two vertices in this shape with a straight line so I can create two new polygons which have the same number of sides. Which vertices could I join? 𝐵 and 𝐹, 𝐴 and 𝐸, 𝐵 and 𝐸, or 𝐴 and 𝐶.

In this question, we have to join two vertices from the given shape with a straight line to create two new polygons which both have the same number of sides. If we join the vertices 𝐵 and 𝐹, we get two new polygons. But do they both have the same number of sides? One of our polygons has three sides. The other has five sides. So we know it’s not 𝐵 and 𝐹.

If we join the two vertices 𝐴 and 𝐸, we get two new polygons. And again, one of our polygons is a triangle with three sides, and the other shape has five sides. One, two, three, four, five. What happens if we join the vertices 𝐵 and 𝐸? We’ve made two new polygons, and it looks like they both have the same number of sides. One, two, three, four. And our second new polygon also has one, two, three, four sides.

If we join the two vertices 𝐵 and 𝐸 in this shape, we can create two new polygons which have the same number of sides. Both have four sides. We joined vertices 𝐵 and 𝐸.