# Isometry

• January 18th 2007, 06:39 PM
symmetry
Isometry
What is isometry in high school geometry?

Do you have one or two sample questions?
• January 18th 2007, 06:46 PM
ThePerfectHacker
Quote:

Originally Posted by symmetry
What is isometry in high school geometry?

Do you have one or two sample questions?

An isometry is a function (or a transformation) such that preserves distance.

For example,
A rotation is an isometry.

Becuase if two points are rotated their new image is the same distance are it was before.
• January 18th 2007, 09:15 PM
CaptainBlack
Quote:

Originally Posted by ThePerfectHacker
An isometry is a function (or a transformation) such that preserves distance.

For example,
A rotation is an isometry.

Becuase if two points are rotated their new image is the same distance are it was before.

Rotation, Translation and Reflection. IIRC all others Isometries of the plane can be generated by
a composition of these.

RonL
• January 19th 2007, 05:14 AM
OReilly
Quote:

Originally Posted by symmetry
What is isometry in high school geometry?

Do you have one or two sample questions?

Isometry is a bijective function (transformation) which transforms figure $F_1$ into figure $F_2$ while preserving congruence of line segments.

Formally, for every two pair of points $(A,B)$ and $(A_1,B_1)$
$I(A) = A_1 \wedge I(B) = B_1 \Rightarrow A_1 B_1 = AB$
• January 19th 2007, 12:51 PM
symmetry
Okay
Good replies.

OReilly, don't get too technical.

Let's keep things simple.
• January 19th 2007, 01:49 PM
OReilly
Quote:

Originally Posted by symmetry
Good replies.

OReilly, don't get too technical.

Let's keep things simple.

You couldn't get simpler than that.

You had to learn first functions and congruence in order to learn isometry.

And math isn't simple... :)
• January 23rd 2007, 05:27 PM
symmetry
Yes...
Math is not simple.

You are right, OReilly.