Discover Mathematics P4: Term 2, Unit 12, Lessons 1–5
GoalName polygons by their sides and vertices, and tell a point, a line, a line segment and a ray apart.
New words
polygon · a closed flat shape made only of straight sidesvertex · a corner where two sides meet; more than one are called verticesray · a part of a line with one endpoint that goes on for ever in one directionline segment · a part of a line with two endpoints
Explanation
A polygon is a flat shape that is closed and has only straight sides. A circle is not a polygon because it has a curved side, and a zigzag that is not closed is not a polygon either. The sides meet at corners called vertices, and a polygon always has as many vertices as sides. We name polygons by the number of sides: triangle 3, quadrilateral 4, pentagon 5, hexagon 6, octagon 8. Now look at straight figures. A point is an exact place, drawn as a dot with a capital letter. A line goes on for ever in both directions and has no endpoints. A line segment is the part of a line between two endpoints. A ray starts at one endpoint and goes on for ever in one direction. We name a ray by its endpoint first: ray EF starts at E and passes through F.
Worked examples
Which of these shapes are polygons? The triangle and the hexagon are polygons: they are closed and all their sides are straight. The circle is not a polygon because its edge is curved.
Polygon
Sides
Vertices
triangle
3
3
quadrilateral
4
4
pentagon
5
5
hexagon
6
6
octagon
8
8
Count sides and vertices. They are always equal. A triangle has 3 sides and 3 vertices, a quadrilateral has 4 and 4, a pentagon 5 and 5, a hexagon 6 and 6, an octagon 8 and 8.
Tell a line, a segment and a ray apart. Line AB has arrows at both ends because it never stops. Segment CD stops at C and D. Ray EF starts at E, passes through F and goes on, so it has an arrow at one end only.
Class activity
Shape hunt. Walk around your home or school and find an object for each polygon: a triangle, a quadrilateral, a pentagon, a hexagon and an octagon (a stop sign is an octagon). Draw each one and write its number of sides and vertices. Then draw a line, a segment and a ray with a ruler and name them.
Practice
1
Name this polygon and say how many sides and vertices it has.
An octagon: 8 sides and 8 vertices.
2
Is a shape with one curved side a polygon? Why?
No. All the sides of a polygon must be straight.
3
What is the difference between a line segment and a ray?
A segment has two endpoints. A ray has one endpoint and goes on for ever in one direction.
4
A polygon has 4 vertices. How many sides does it have and what is it called?
4 sides: a quadrilateral, because a polygon has as many sides as vertices.
5
Menna says a line has two endpoints. Is she right?
No. A line goes on for ever in both directions, so it has no endpoints. A segment has two endpoints.
