Video Transcript
Determine whether the following
polygon is convex or concave.
Now we have a number of ways to
identify whether a polygon is convex or concave. Beginning with this simple
definition, we say a polygon is convex if all of its interior angles are less than
180 degrees. And it will be said to be concave
if at least one angle is greater than 180 degrees. And so, we could go through our
shape and look at all of the interior angles. We’d want to find at least one
that’s greater than 180 degrees, in other words, a reflex interior angle.
But there is another way. And that is to construct the
diagonals of the shape. To do so, we join nonadjacent
vertices. So, for example, we have a diagonal
here, one here, another here, and we’re going to continue by adding all of the
diagonals to our shape. When we’re done, each vertex has
three diagonals coming off of it. For a convex polygon, all of these
diagonals should lie inside the shape itself, whereas with a concave polygon, at
least one of them will lie outside.
Now, actually, if we look at our
shape, we see that no matter the color of the line we’ve drawn — whether the
diagonal is a green line, a yellow line, or a pink line — they all lie within the
shape itself. And so, we can say that this shape
is convex.
