Page 2: Special Cases and Properties

The second page explores special cases of homothetic transformations and their unique properties, focusing on ratios of 1 and -1.

Highlight: Two significant special cases of homothétie rapport agrandissement réduction are presented:

1. When ratio k=1: The transformed figure perfectly overlaps with the original
2. When ratio k=-1: The transformation results in central symmetry

Example: Two specific demonstrations are provided:

1. Triangles ABC and A'B'C' superimposed when k=1
2. Triangle A'B'C' as a central symmetry of ABC when k=-1

Definition: Central symmetry occurs when the ratio is -1, creating a mirror image through the center point O.

Vocabulary:

• Symétrie centrale: Central symmetry
• Figures superposées: Superimposed figures
• Image: The resulting transformed figure

Page 1: Introduction to Homothety

The first page introduces the fundamental concepts of homothety and its basic properties. The transformation is explained through its defining characteristics and practical examples.

Definition: Homothety is a geometric transformation that enlarges or reduces geometric figures, defined by a center point and a ratio.

Highlight: The ratio k determines the nature of the transformation:

• When k>0: positive ratio (enlargement)
• When k<0: negative ratio (reduction)

Example: Two triangles are presented to demonstrate exemples d'homothétie mathématiques:

1. Triangle A'B'C' as an enlargement of ABC with center O and ratio k=0.5
2. Triangle A'B'C' as a reduction of ABC with center O and ratio k=-0.5

Vocabulary:

• Homothétie: A geometric transformation that scales figures
• Rapport: The ratio determining the scale factor
• Centre: The fixed point around which the transformation occurs