There are two topics in Geometry that can sometimes be difficult for students. The first one is the study of transformations and the second is symmetry. Hopefully this review can be useful for you, your classmates, and your Irvine tutor!

TRANSFORMATIONS
There are four different types of transformations in Geometry:

1. Rotation: Rotation is turning around a center. In Geometry, the distance from the center to any point on the shape stays the same during rotation. And every point makes a circle around the center.

2. Reflection: A reflection in Geometry is a flip over a line. Every point is the same distance from the central line and the reflection has the same size as the original image. The central line is also called the mirror line. Reflections in Geometry can occur both vertically and horizontally.

3. Translation: In Geometry, translation simply means moving without rotating, resizing, or anything else. In Geometry it simply means moving. For a shape to be translated, every point of the shape must be moved in the same direction at the same distance.

4. Resizing: Shapes can be resized in Geometry by either being made bigger or smaller, but the shape will still be similar. In order for this to happen in Geometry, the angles must stay the same and all relative sizes are still the same (proportional). Note that some Geometry tutors or teachers may also call this dilation, contraction, compression, enlargement, or expansion, but it is all just resizing.

SYMMETRY
In Geometry there are also four different types of Symmetry:

1. Reflection symmetry: Reflection symmetry is easily recognizable in Geometry because one side is the exact reflection of the other half. The line of symmetry is directly down the middle and is also called the mirror line (as mentioned above). Not all shapes have lines of symmetry and some may have more than one line of symmetry. In Geometry, a square has two lines of symmetry. It is symmetric both vertically and horizontally.

2. Rotational symmetry: When a shape or object is rotationally symmetric in Geometry, it will look the same even if it is rotated. Circles are good examples of Geometric shapes that have rotational symmetry.

3. Point symmetry: Something that has point symmetry in Geometry looks like same upside-down or from two opposite directions. The Geometry rules are; every part must have a matching part. The matching part must be the same distance from the central point but in the opposite direction.

4. Lines of symmetry of Plane shapes: You can use the help of your Irvine Geometry tutor to see if a plane shape is symmetric by doing a simple test. If you can fold it or imagine folding it and all the sides add up, then the shape is symmetric.

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