Points, Lines and Planes

Slideshow 43, Mathematics

Mr Richard Sasaki

Room 307

OBJECTIVES

• RECALL NAMES OF SOME COMMON 3D SHAPES

• UNDERSTAND THE MEANING OF A POINT, LINE AND PLANE AND NOTATION USED

• USE THESE PROPERTIES TO ANSWER PROBLEMS

SOME SIMPLE 3-D SHAPES

Sphere Cylinder Cone

Square-based pyramid

Hemisphere

PLATONIC SOLIDS / CONCAVE REGULAR POLYHEDRONS

Tetrahedron Cube Octahedron

Dodecahedron Icosahedron

PRISMS

CuboidTriangular Prism Pentagonal

Prism

Hexagonal Prism

Octagonal Prism

Decagonal Prism

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 point is different to a vertex…any ideas how?)A

A vertex is usually used to connect lines and line segments. A point may be separate. A vertex is a type of point.

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 vertices, we can just simply name a line at times.

PLANES

What is a plane?No it doesn’t fly in the sky! A plane is a flat 2D surface. It is often thought of to be infinite in length. 𝑝

As with lines, we can simply name them but they may be named about their vertices if stated (eg: ABCD).

INTERSECTION

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!)

PARALLEL ELEMENTS

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.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 and planes can also be parallel as long as a parallel line of points on the plane are always equal distance to the physical line.For this figure, as an example.

ANSWERS - EASY

𝐷𝐶 ,𝐸𝐹 ,𝐺𝐻

Face DCFE𝐺𝐸 ,𝐻𝐹 ,𝐸𝐷 ,𝐹𝐶(Opposite order of letters is okay.)

𝐴𝐷 ,𝐷𝐶

1 – 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 - HARD

45o

One

2222

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.

No, the pencil must sit on the line but it can at any angle perpendicular to the line.