Geometric Transformations in Mathematics
This page presents a comprehensive overview of five fundamental geometric transformations, essential for students preparing for the Brevet des collèges mathematics exam. Each transformation is illustrated with a diagram and a brief explanation, making it an excellent Fiche révision brevet maths PDF 2023 resource.
Axial Symmetry
The first transformation discussed is axial symmetry. The diagram shows a point F and its image F' reflected across an axis (d). This transformation is crucial in understanding reflections and mirror images in geometry.
Definition: Axial symmetry is a transformation that reflects a figure across a line, creating a mirror image.
Translation
The second transformation illustrated is translation. The diagram depicts a point F being moved to a new position F' through a translation vector.
Vocabulary: A translation is a transformation that moves every point of a figure the same distance in the same direction.
Homothety
Homothety is the third transformation presented. The diagram shows a point F being transformed to F' with respect to a center O.
Highlight: Homothety is a transformation that enlarges or reduces a figure while maintaining its shape, often used in scaling problems.
Central Symmetry
The fourth transformation is central symmetry. The diagram shows a triangle ABC being transformed into A'B'C' around a center point O.
Example: In central symmetry, each point of the original figure is rotated 180° around the center point.
Rotation
The final transformation discussed is rotation. The diagram illustrates a triangle ABC being rotated 30° counterclockwise around a center point to form A'B'C'.
Vocabulary: Rotation is a transformation that turns a figure around a fixed point by a certain angle.
This page serves as an excellent Fiche de révision maths 3ème brevet, providing clear visual representations and concise explanations for each geometric transformation. It's particularly useful for students reviewing Exercices brevet maths par thème related to transformations and symmetry.