Transformation is the process of changing the position, size, or shape of a figure while maintaining its properties. There are four main types of transformations: translation, reflection, rotation, and dilation.
Translation is when a figure is moved from one position to another without changing its size or shape. This is done by shifting the figure along a straight path.
Reflection is when a figure is flipped over a line, called the line of reflection. The original figure and its reflection are mirror images of each other.
Rotation is when a figure is turned around a point, called the center of rotation. The angle of rotation determines the amount and direction of the turn.
Dilation is when a figure is enlarged or reduced in size. This is done by multiplying the coordinates of each point by a scale factor.
Congruence is a term used to describe figures that have the same size and shape. Two figures are congruent if they can be matched exactly by a series of transformations. Congruent figures have corresponding angles and side lengths that are equal.
In order to prove two figures are congruent, it is important to show that all corresponding angles and side lengths are equal. This can be done through various methods such as using the SAS (side-angle-side), ASA (angle-side-angle), SSS (side-side-side), or AAS (angle-angle-side) postulates.
Overall, understanding transformation and congruence is essential in geometry as it helps us analyze and identify relationships between figures in a systematic way.
Lesson 12 transformation and congruence
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