Congruence Transformation
A congruence transformation, also known as a congruence or isometry, refers to a type of transformation in geometry that preserves the shape and size of a figure
A congruence transformation, also known as a congruence or isometry, refers to a type of transformation in geometry that preserves the shape and size of a figure. In other words, when a figure undergoes a congruence transformation, it moves and rotates in a way that maintains its congruent relationship with the original figure.
There are three main types of congruence transformations: translations, rotations, and reflections.
1. Translation: A translation is a transformation that moves every point in a figure the same distance and direction. It preserves the size and shape of the figure but changes its position in the plane.
2. Rotation: A rotation is a transformation that rotates a figure around a fixed point called the center of rotation. It preserves the size and shape of the figure but changes its orientation.
3. Reflection: A reflection is a transformation that flips a figure over a line called the line of reflection. It preserves the size and shape of the figure but changes its orientation.
To determine if two figures are congruent, we can use congruence transformations by applying the appropriate sequence of translations, rotations, and reflections to one figure to make it coincide with the other figure. If the figures overlap perfectly after the transformation, they are congruent.
Congruence transformations are significant in geometry because they allow us to establish congruence between figures without the need for measurements. By using these transformations, we can prove geometric properties, solve problems, and demonstrate the equality of different geometric objects.
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