Perpendicular Lines and Euclid's Theorems

This page focuses on teorema di euclide: formule and perpendicular lines concepts.

Definition: Euclid's theorems specifically apply to right triangles:

1. A leg is the mean proportional between the hypotenuse and its projection
2. The height is the mean proportional between the projections of the legs

Highlight: For perpendicular lines, if one line has an angular coefficient m₁, the other line will have a coefficient m₂ where m₁ * m₂ = -1.

Understanding Triangle Similarity Criteria and Parallel Lines

This page introduces the fundamental concepts of criteri di similitudine triangoli and parallel lines intersected by transversals. The content begins with a detailed explanation of how transversal lines create different types of angles when intersecting parallel lines.

Definition: A transversal line crossing two parallel lines creates eight distinct angles.

The three similarity criteria are explained:

1. First criterion requires two corresponding angles to be congruent
2. Second criterion involves two angles and the included side
3. Third criterion requires all three sides to be proportional

Vocabulary: Alternate angles (alterni), corresponding angles (corrispondenti), and conjugate angles (coniugati) are the three main types of angles formed.

Highlight: Understanding these angle relationships is crucial for applying the primo criterio di similitudine.