Andalusia PAU Technical Drawing Applied to Plastic Arts and Design II study plan

Construct the fourth proportional and the third proportional of two given segments using Thales' intercept theorem, with compass-and-straightedge accuracy to ±1 mm.

Divide a segment into n equal parts and into parts proportional to given ratios, verifying the construction by measuring each resulting part.

Apply the geometric mean (altitude and leg theorems) to build a segment of length √(a·b) and confirm the result numerically.

Draw the harmonic conjugate of a point with respect to a segment and state the cross-ratio value that defines it.

Construct similar figures given a similarity ratio, using homothety from an external centre, and check that all corresponding lengths scale by the stated factor.

Solve an inverse similarity (figure similar to a given one with a rotated orientation) by composing a homothety with a rotation about a chosen centre.

Produce the equivalent triangle of a given polygon and then the equivalent square, verifying equal areas by computation.

Apply a translation, a rotation, and an axial symmetry in sequence to a polygon and describe the resulting isometry as a single transformation where possible.

Solve tangency problems between circumferences and lines using the dilation (centre-of-similitude) method, including the external and internal tangent cases.

Draw the common tangents to two circles of unequal radius and mark the tangent points precisely.

Construct the tangent lines to a circle from an external point and prove the right-angle condition at each tangent point.

Resolve a mixed tangency (circle tangent to a line and to another circle, passing through a given point) using inversion or auxiliary-circle methods.

Construct an ellipse from its foci and major axis using the string/pins method and the concentric-circle method, and compare the two results.

Draw the tangent and normal to an ellipse at a given point using the focal property (equal angles with the focal radii).

Construct a parabola given its focus and directrix, and a hyperbola given its foci and transverse axis, plotting at least ten points on each.

Draw the tangent to a parabola and to a hyperbola at a specified point and state the geometric property used in each case.

Represent points in all four dihedral quadrants and determine their symmetric images with respect to the horizontal plane, the vertical plane, and the ground line.

Determine the true length and the angles to the reference planes of a given line by the right-triangle (difference-of-coordinates) method.

Find the intersection point of a line with a plane given by its traces, and decide visibility of the line on each side of the plane.

Construct the intersection line of two planes given by their traces, handling the case where traces meet outside the drawing area.

Draw a line parallel to a given line through a point, and a plane parallel to a given plane through a point, using the trace method.

Construct a perpendicular from a point to a line and from a point to a plane, and verify perpendicularity using the theorem of the right angle.

Obtain the true magnitude of a segment by the change-of-plane method and by the rotation method, and confirm both give the same length.

Determine the shortest distance from a point to a plane and between two skew lines, expressing each result as a true-magnitude segment.

Draw the dihedral representation of a regular tetrahedron, cube, and octahedron resting on a face or an edge, and identify hidden edges correctly.

Construct the section of a cylinder and of a cone by an oblique plane, showing the resulting ellipse or parabola in true shape.

Build an isometric axonometric projection of a simple polyhedron from its orthographic views, applying the correct axis angles and coefficient of reduction.

Produce a cavalier (oblique) perspective of the same solid with a stated reduction factor on the receding axis, and compare it with the isometric result.

Apply the UNE/ISO conventions for line types (visible, hidden, centre, cutting-plane) to redraw one earlier exercise to standard.

Dimension a multi-view drawing completely and without redundancy, choosing a scale from the standard series (1:1, 1:2, 1:5, 2:1) and stating it in the title block.

Produce a freehand sketch of a given solid within 10 minutes, keeping proportions within roughly 10% of the original.

Complete a timed 60-minute mock paper covering proportionality, tangency, and a conic, and self-mark it against a written checklist.