Year 10+ Plane Geometry
Chapters
Transformations
Transformations
There are four important geometric transformations. These are slides, flips, turns and enlargement, technically known as translation, reflection, rotation and dilation.
Slides, Flips and Turns
Slide: In this transformation, the object is pushed along (without changing the lengths of any of its lines or the directions they point in)
to another place.
translation.
Flip: this is like looking at the object in the mirror. You can flip in different directions by putting the mirror in different places.
The object is still the same
size and shape after it has been flipped, just backwards somehow.
reflection.
Turn: this is spinning the object. Pick a point either inside or outside the object and spin the object around that point. If the point is outside the object, it's like
spinning a tennis ball around in a stocking. If the point is inside the object, it's like sticking a pin in the object and spinning it around that point like a wheel spins around its axle.
The object is still the same size and shape after it has been turned.
rotation.
After applying any of these three transformations, or any combination of them, the object still has the same size, area, angles, and side-lengths.
Enlargement (Blowing Things Up)
This transformation changes the size of objects. We use the term, "enlargement", to either mean making something bigger or making it smaller. The angles and the relative sizes of parts of the object (when compared to the rest of the object) remain the same. Some other words for this transformation are dilation, resizing, epxansion, contraction and compression.
Similarity and Congruence
Two shapes are congruent if one can be turned into the other using only the reflection, rotation and translation transformations.
If enlargement is also needed to turn one shape into another, then the two shapes are called similar.
Description
In these chapters you will learn about plane geometry topics such as
- Area (Irregular polygons, plane shapes etc)
- Perimeter
- Conic sections (Circle, Ellipse, Hyperbola etc)
- Polygons (Congruent, polygons, similar, triangles etc)
- Transformations and symmetry (Reflection, symmetry, transformations etc)
etc
Even though these chapters are marked for Year 10 or higher students, several topics are for students in Year 8 or higher
Audience
Year 10 or higher, suitable for Year 8 + students as well.
Learning Objectives
Learn about Plane Geometry
Author: Subject Coach
Added on: 28th Sep 2018
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