GEOMETRY TOPICS

Transformations

Rotation Turn!

Reflection Flip!

Translation Slide!

After any of these transformations (turn, flip or slide), the shape still has the same size so the shapes are congruent.

Rotations

Rotation means turning around a center.

The distance from the center to any point on the shape stays the same. The rotation has the same size as the original shape.

Here a triangle is rotated around the point marked with a "+"

Translations

In Geometry, "Translation" simply means Moving. The translation has the same size of the original shape.

To Translate a shape:

Every point of the shape must move:

 the same distance  in the same direction.

Reflections

A reflection is a flip over a line. In a Reflection every point is the same distance from a central line. The reflection has the same size as the original image.

The central line is called the Mirror Line ...

Mirror Lines can be in any direction.

Reflection Symmetry

Reflection Symmetry (sometimes called Line Symmetry or Mirror Symmetry) is easy to see, because one half is the reflection of the other half.

Here my dog "Flame" has her face made perfectly symmetrical with a bit of photo magic.

The white line down the center is the Line of Symmetry (also called the "Mirror Line")

The reflection in this lake also has symmetry, but in this case:

-The Line of Symmetry runs left-to-right (horizontally)

-It is not perfect symmetry, because of the lake surface.

Line of Symmetry

The Line of Symmetry (also called the Mirror Line) can be in any direction.

But there are four common directions, and they are named for the line they make on the standard XY graph.

Line of Symmetry Example Shape

Similar Shapes

Two shapes are Similar when the only difference is size (and possibly the need to move, turn or flip one around).

Resizing

When you resize a shape it

gets bigger or smaller.

... but it still looks similar:

 all angles stay the same  relative sizes are in proportion to each other

Other terms for resizing are dilation, contraction, compression, enlargement or even expansion! Same idea, just different names.

If one shape can become another using Resizing , the shapes are Similar:

These Shapes are Similar!