Catalonia PAU Technical Drawing (Dibuix Tècnic II) flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Thales' theorem

An angle inscribed in a semicircle is a right angle. The midpoint of the hypotenuse of a right triangle is equidistant from all three vertices.

Ellipse focal property

The sum of distances from any point on the ellipse to the two foci is constant and equals the major axis length 2a. The minor semiaxis satisfies b² = a² − c².

Parabola tangent bisector

At any point P on a parabola, the tangent bisects the angle between the focal radius PF and the line through P parallel to the axis of symmetry.

Hyperbola asymptotes

For a hyperbola with transverse semiaxis a and conjugate semiaxis b, the asymptotes pass through the center with slopes ±b/a, where b² = c² − a².

Common external tangent construction

To draw a common external tangent to two circles, construct an auxiliary circle centered at the larger center with radius R−r, draw tangents from the smaller center to it, then offset.

Inversion of a circle

Under inversion centered at O, a circle not passing through O maps to another circle; a circle passing through O maps to a line not passing through O.

Point dihedral projections

A point's horizontal projection lies below the ground line at a distance equal to its height above the horizontal plane; its vertical projection lies above the ground line at a distance equal to its depth from the vertical plane.

True length by right triangle

The true length of a segment equals the hypotenuse of a right triangle whose legs are the segment's projection and the difference in distances of its endpoints to the projection plane.

Line perpendicular to plane

A line perpendicular to a plane has its horizontal projection perpendicular to the plane's horizontal trace and its vertical projection perpendicular to the vertical trace.

Plane intersection by traces

The intersection line of two planes passes through the piercing points where the trace lines of one plane meet the other plane.

Change of projection plane

To change a projection plane, draw a new ground line, project each point perpendicular to it, and transfer the distance from the old plane measured parallel to the new ground line.

Euler's polyhedron formula

For any convex polyhedron, the number of vertices V, edges E, and faces F satisfy V − E + F = 2.

Regular tetrahedron volume

For a regular tetrahedron of edge a, the volume is a³/(6√2) and the height is a√(2/3), approximately 0.8165a.

Cone lateral area

The lateral surface area of a right cone is πrg, where r is the base radius and g is the slant height; the total area adds the base area πr².

Cone development sector

The development of a right cone is a circular sector of radius equal to the slant height g and central angle θ = 360°·(r/g).

Sphere plane section

A plane cutting a sphere at distance d from its center produces a circle of radius √(r²−d²), where r is the sphere radius.

Polyhedron section construction

To find a plane section of a polyhedron, locate where the cutting plane intersects each edge, then connect points lying on the same face; the result is a polygon.

First-angle projection arrangement

In first-angle projection, the object lies between the observer and the projection plane; the view from the left is placed on the right and the top view below the front view.

Dimension line placement

Dimension lines are drawn parallel to the measured edge with arrowheads at both ends; numerals sit above the line, centered, and are never crossed by any line.

Scale notation

Scale is the ratio of drawing length to real length, written as 1:n for reduction or n:1 for enlargement; it is stated in the title block.

Section hatching convention

Cut surfaces are hatched with thin continuous lines at 45° to the main outline; adjacent parts use opposite directions or different spacings.

Half-section view

A half-section shows one half of a symmetrical object in section and the other half in outside view, separated by a center line; hidden lines are usually omitted.

Isometric axes and scale

Isometric projection uses three axes at 120° with a foreshortening factor of √(2/3) ≈ 0.816; isometric drawing uses full scale along the axes for convenience.

Cabinet oblique projection

Cabinet projection draws the front face true shape and the receding axis at 45° with half scale, reducing distortion compared with cavalier projection.

Two-point perspective

In two-point perspective, vertical lines remain vertical and horizontal lines parallel to two principal directions converge to two vanishing points on the horizon line.

Isometric circle ellipse axes

In isometric projection, a circle of diameter d in a coordinate plane becomes an ellipse with major axis 1.22d and minor axis 0.71d.

Flowchart decision symbol

In a flowchart, a decision is represented by a diamond; process steps use rectangles, start/end use ovals, and input/output uses parallelograms.

CAD relative coordinates

In CAD, relative coordinates are entered as @dx,dy, where dx and dy are offsets from the last point; polar coordinates use @distance<angle.

CAD object snaps

Object snaps such as endpoint, midpoint, center, intersection, and perpendicular constrain the cursor to exact geometric points, ensuring precision.

Bar chart baseline rule

In a bar chart, bar length is proportional to value; the baseline must start at zero, otherwise relative differences are visually exaggerated and misleading.

Pencil grades for drawing

Use 2H or harder for construction and guide lines, and HB or B for final visible outlines; compass leads are sharpened to a chisel point.

Line hierarchy in technical drawing

Visible outlines are thick continuous lines; hidden edges are dashed; center lines are chain lines; dimension and hatching lines are thin continuous lines.