Italy Secondaria di secondo grado – classe 2ª Geometric disciplines

1. Geometric drawing

Euclidean elements and conventions · Orthographic and axonometric projection · Intuitive perspective

• Geometric Constructions: Drawing Exactly with Compass and Straightedge – A geometric construction draws a figure exactly using only a compass and a straightedge (a ruler used for straight lines). Key constructions: the perpendicular bisector of a segment, the bisector of an angle, a perpendicular from a point to a line, angles of 60°, 30°, 90° and 45°, a triangle from three sides (SSS), two sides and the included angle (SAS) or two angles and a side (ASA), and regular polygons such as the hexagon. Each works because equal compass arcs make equal lengths, which give congruent triangles.
• Orthographic Views of Solids – An orthographic view shows a solid as seen straight on from one direction, with no perspective. The three main views are the front view (front elevation), the top view (plan) and the side view (side or end elevation). Each view loses one dimension, so we usually need all three to fix the shape. Views are arranged in a standard layout: first-angle projection (plan below the front view; used in India, Europe and ISO standards) or third-angle projection (plan above; used in the USA). Visible edges are thick continuous lines, hidden edges are dashed, and centre lines are chain lines. A net is the flat pattern that folds into a solid, and a cross-section is the shape you see when you cut through it.
• Perspective Drawing: Horizon, Vanishing Points and Shadows – Perspective drawing makes a flat page look deep. You draw a horizon line at eye level, then lines going away from you meet at vanishing points. Far objects are drawn smaller (size ∝ 1 ÷ distance). One-point perspective uses one vanishing point, two-point uses two. Shadows are found with two crossing lines.