a Consider the conditions for a shape to be a polygon when examining the given figure.
B
b Consider the conditions for a shape to be a polygon when examining the given figure.
C
c Consider the conditions for a shape to be a polygon when examining the given figure.
D
d Consider the conditions for a shape to be a polygon when examining the given figure.
E
e Consider the conditions for a shape to be a polygon when examining the given figure.
F
f Consider the conditions for a shape to be a polygon when examining the given figure.
G
g Consider the conditions for a shape to be a polygon when examining the given figure.
H
h Consider the conditions for a shape to be a polygon when examining the given figure.
A
a Not a polygon. See solution.
B
b It is a polygon. See solution.
C
c Not a polygon. See solution.
D
d It is a polygon. See solution.
E
e Not a polygon. See solution.
F
f It is a polygon. See solution.
G
g It is a polygon. See solution.
H
h Not a polygon. See solution.
Practice makes perfect
a For a shape to be a polygon, three things things must be fulfilled.
It is a two-dimensional closed figure.
It is made up of straight line segments connected end-to-end.
The segment may not cross (intersect) at any other point.
Examining the given shape, we see that it has a curved segment — which means it is not a polygon.
b Examining the shape, we see that it is a two-dimensional closed figure made up of straight lines connected end-to-end. Furthermore, none of the segment crosses each other. Therefore, we know that this is a polygon. Since it has three vertices, it is called a triangle.
c Examining the shape, we see that it is a two-dimensional closed figure made up of straight lines connected end-to-end. However, one of the segments crosses two other segments. Therefore, this cannot be a polygon.
d Examining the shape, we see that it is a two-dimensional closed figure made up of straight lines connected end-to-end. Furthermore, none of the segment crosses each other. Therefore, we know that this is a polygon and since it has five vertices it is called a pentagon.
e Examining the shape, we see that it is a two-dimensional closed figure made up of straight lines. However, it is not connected end-to-end. Therefore, this cannot be a polygon.
f Examining the shape, we see that it is a two-dimensional closed figure made up of straight lines connected end-to-end. Furthermore, none of the segment crosses each other. Therefore, we know that this is a polygon.
g Examining the shape, we see that it is a two-dimensional closed figure made up of straight lines connected end-to-end. Furthermore, none of the segment crosses each other. Therefore, we know that this is a polygon. Because it has four vertices, this is a quadrilateral.
It looks like a trapezoid, because it would seem like it has two parallel sides. However, this is not explicitly stated in the exercise and therefore we cannot say that it is a trapezoid.
h Examining the shape, we see that it is a two-dimensional figure made up of straight lines. However, since the shape is not closed, it cannot be a polygon.
