Points, Lines and PlanesSlideshow 43, Mathematics

Mr Richard SasakiRoom 307

OBJECTIVES• Recall names of some common 3D Shapes

• Understand the meaning of a point, line and plane and notation used

Sphere Cylinder Cone

Square-based pyramid

Hemisphere

Some Simple 3D Shapes

Tetrahedron Cube Octahedron

Dodecahedron Icosahedron

Convex regular polyhedra are also known as the platonic solids.

Convex Regular Polyhedra

CuboidTriangular Prism Pentagonal

Prism

Hexagonal Prism

Octagonal Prism

Decagonal Prism

Prisms

PointsWhat 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.

How is a point different to a vertex?A

A vertex is used to connect things. A point may be not touching anything. A vertex is a type of point.

𝐴 𝐵 𝐶

What is a line?We already know this. It is infinite in length and travels in opposite directions about its centre.

𝑙As we’re not always interested in points, we can just simply name a line at times.

Lines

This line can be named , or .𝐴𝐵𝐴𝐶 𝐵𝐶If three or more points exist on a line, they are .collinear

What is a plane?A plane is a flat 2D surface. It is usually thought to be infinite in length. 𝑝As with lines, we can simply name them (the plane above is named) but they may be named about their vertices (eg: ) if it is thought to be finite in size.

Planes

𝐴 𝐵𝐷 𝐶

A plane infinite in size can be named about three points on the plane.

𝑞𝑍 𝑌𝑋

Plane can be named plane .

Note: Three or more points on a plane are said to be coplanar.

Answers

, and , , and

and

Plane , ,, and , and

Look at the two intersecting planes below.

We call the line formed between them the

.line of intersection

(The planes don’t have to be perpendicular to intersect, remember!)

Intersections

In the land of 3D, any two pairs of lines that never touch must be parallel. Is this true?No! They must always be the same distance apart at all points.

We call lines that are not parallel and never touch

.skew lines

Parallel Elements

Are these lines parallel (by appearance)?

𝑙𝑚

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.

For this figure, Face as an example.

Parallel Elements

𝐺𝐷𝐶𝐻

𝑙𝑝

𝐷𝐶 ,𝐸𝐹 ,𝐺𝐻

Face 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.

Answers - Easy

Answers - HardOne pair (two faces)

2222

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.

45𝑜