1. Points, Lines and Planes
Slideshow 43, Mathematics
Mr Richard Sasaki

2. Objectives Recall names of some common 3D Shapes
Understand the meaning of a point, line and plane and notation used

3. Some Simple 3D Shapes Sphere Cylinder Cone Square-based pyramid
Hemisphere

4. Convex Regular Polyhedra
Tetrahedron
Cube
Octahedron
Dodecahedron
Icosahedron
Convex regular polyhedra are also known as the platonic solids.

5. Prisms Triangular Prism Cuboid Pentagonal Prism Hexagonal Prism
Octagonal Prism
Decagonal Prism

6. Points
What is a point?
A point is represented by a dot and its name. It has zero size in all directions.
So what does it have?
Position only. A
How is a point different to a vertex?
A vertex is used to connect things. A point may be not touching anything. A vertex is a type of point.

7. Lines
What is a line?
We already know this. It is infinite in length and travels in opposite directions about its centre. 𝑙
As we’re not always interested in points, we can just simply name a line at times. 𝐴 𝐵 𝐶
This line can be named , or 𝐴𝐵 𝐴𝐶 𝐵𝐶
If three or more points exist on a line, they are
collinear

8. Planes Note: Three or more points on a plane are said to be coplanar.
What is a plane?
A plane is a flat 2D surface. It is usually thought to be infinite in length. 𝐴 𝑝 𝐵 𝐷 𝐶
As with lines, we can simply name them (the plane above is named 𝑝) but they may be named about their vertices (eg: 𝐴𝐵𝐶𝐷) if it is thought to be finite in size. 𝑞
A plane infinite in size can be named about three points on the plane. 𝑍 𝑌 𝑋
Plane 𝑝 can be named plane 𝑋𝑌𝑍.

9. 𝐷, 𝐸 and 𝐹
𝐴, 𝐵, 𝐶 and 𝐷
𝐷𝐸 , 𝐷𝐹 and 𝐸𝐹
Plane 𝐴𝐵𝐶, 𝐴𝐵𝐷, 𝐴𝐶𝐷, 𝐵𝐶𝐷
𝐸 and 𝐹
𝐴, 𝐵 and 𝐶

10. Look at the two intersecting planes below.
Intersections
Look at the two intersecting planes below.
We call the line formed between them the
line of
intersection
(Planes don’t have to be perpendicular to intersect, remember!)

11. Parallel Elements
Any two pairs of lines that never touch must be parallel. Is this true?
No! Not in 3𝐷 anyway. They must always be the same distance apart at all points.
We call lines that are not parallel and never touch
skew lines

12. Parallel Elements 𝑙 𝑚 Are these lines parallel (by appearance)?
How about these planes?
Lines can be parallel to planes as long as a parallel line of points on the plane are always equal distance to the line. 𝑙 𝑝
For this figure, 𝐹𝐸 ∥ Face We can make many statements like this.
𝐺𝐷𝐶𝐻

13. 𝐷𝐶 , 𝐸𝐹 , 𝐺𝐻
Face 𝐷𝐶𝐹𝐸
𝐸𝐺 , 𝐹𝐻 , 𝐷𝐸 , 𝐶𝐹
𝐴𝐷 , 𝐷𝐶
1 line. The line of intersection.
Yes, the plane must be flat so the flat line will lie on it.
A circle.
A train track / ladder / fence / rack.

14. One pair (two faces) 2 2 2 2
10 (on each plane)
The sphere only has one curved face. A straight line or flat plane will have differing distances from the sphere’s surface.
No, because it has one flat surface.
45 𝑜