Canary Islands PAU Technical Drawing II common mistakes
Canary Islands PAU Technical Drawing II · Understand the traps and how to avoid them.
When reducing a figure by a negative or fractional homothety ratio, students place the image on the same side of the centre as the original, or measure the ratio from the image instead of the centre, producing a figure that is inverted or wrongly scaled.
The sign convention (negative ratio = image on the opposite ray through the centre) is taught as a formula but rarely practised with a compass and ruler, so the geometric meaning of the sign is never internalised.
What to do instead
Before drawing anything, mark the centre O and, for each vertex P, draw the full line OP (not just the ray). For k<0 place P' on the opposite side with OP' = |k|·OP; check with a ruler that OP'/OP equals |k| for at least two vertices and that the image is the mirror position about O.
When constructing a triangle from given data, students pick the wrong construction (e.g. attempting a circumcircle when the data specify a side, an adjacent angle and the altitude to that side) and end up with a triangle that satisfies only some of the conditions.
Candidates memorise named constructions in isolation and do not build a decision habit of classifying the given data (SSS, SAS, ASA, side-angle-opposite-side ambiguous case, altitudes, medians) before starting.
What to do instead
Spend 30 seconds writing the given elements and the unknown, then match to a known locus: an angle fixes a ray, a distance fixes a circle, an altitude fixes a parallel line. Construct the loci and intersect them. If the data include a side, an angle and the opposite side, expect two solutions (ambiguous case) and state both.
In tangent problems, students draw a tangent line by eye through an external point to a circle, or construct the tangent to a circle at a point without first drawing the radius to that point, and the line misses tangency by a visible margin.
The classical construction (Thales circle on the segment joining the external point to the centre) is often skipped in favour of estimating, because students do not see why the right angle guarantees tangency.
What to do instead
Always construct: for an external point P and circle centre O, draw the circle with diameter OP; its intersections T with the given circle are the tangent points, since angle OTP is 90°. For tangency at a given point, draw radius OT and erect the perpendicular at T. Verify by checking the perpendicular distance from O to the line equals the radius.
When asked for the true shape of a section of a polyhedron, students draw the section in the projection plane where it appears foreshortened and label it as the true shape, without any rabattement or auxiliary projection.
The section polygon is easy to obtain directly in one view, and students confuse 'visible outline of the cut' with 'true size of the cut', forgetting that a plane oblique to the projection plane distorts lengths and angles.
What to do instead
After finding the section in the given views, project the section onto a plane parallel to the cutting plane (change of projection plane) or rabatt the cutting plane about its trace. Only the view in which the cutting plane appears edge-on (as a line) gives the true shape; state explicitly which view that is.
In multiview problems, students place a third view in the wrong position relative to the first two (e.g. putting the left-side view on the right in first-angle projection, or mixing first- and third-angle layouts within one drawing).
First-angle and third-angle conventions are mirror images of each other, and students learn the 'unfold the box' rule verbally without a fixed mental model, so under time pressure they default to intuition.
What to do instead
Adopt one rule and write it on the sheet: in first-angle the object sits between observer and plane, so the view from the left is drawn on the right; in third-angle the plane sits between observer and object, so the view from the left is drawn on the left. Check alignment: corresponding features must share horizontal or vertical projection lines across all views.
When finding the intersection of a line and a plane (or two planes) in dihedral projection, students extend lines until they 'look like' they cross in the drawing, without using an auxiliary plane or a change of projection plane.
Coincidence in one view is mistaken for actual intersection in space; the third coordinate is ignored because it is not drawn.
What to do instead
Use a projecting auxiliary plane containing the line: find where it cuts the given plane (two points), then transfer those points back to the principal views. Confirm the result by checking the point lies on the line in both views and on the plane in both views.
When dimensioning, students give the same length twice (redundant dimension), dimension to hidden lines, or omit the overall dimensions, and place dimension lines inside the hatched area of a section.
Dimensions are added as an afterthought to make the drawing 'look complete', without applying the rule that each feature is dimensioned once at the view where it is clearest.
What to do instead
Before dimensioning, list the features and assign each exactly one dimension in the view where it shows true length and is not hidden. Add overall length, width and height last and check no chain of dimensions closes a loop. Keep dimension lines outside hatching and off the object outline.
When drawing an ellipse, parabola or hyperbola, students plot a few points by eye and join them with a freehand curve, producing a shape whose focal properties and tangent directions are wrong at the ends.
The constructions (concentric circles, rectangle method, directrix-focus method) are seen as tedious and are replaced by sketching, but conic questions usually test the tangent or the focal distances derived from those constructions.
What to do instead
Construct the curve from its definition: for the ellipse use the concentric-circle or the string/foci method and mark the major and minor axes and foci first; for the parabola use the directrix-focus construction. To draw a tangent at a point, bisect the angle between the focal radius and the line to the directrix (parabola) or use the equal-angle property at the foci (ellipse).
In axonometric or cavalier/cabinet perspective, students apply the same scale to all three axes or draw the receding axis at 30° when the stated axonometric system requires different angles and coefficients, so the object looks plausible but is metrically wrong.
Isometric is over-practised, so students assume every axonometric is isometric and ignore the reduction coefficients and axis angles given in the problem statement.
What to do instead
Read the system named (isometric, dimetric, trimetric, cavalier with q=1/2, cabinet with q=1/2) and set the axes and coefficients first. In isometric the three axes are at 120° with equal coefficients; in cabinet the receding axis is at 45° with half scale. Mark the scale on each axis before drawing any edge.
When a problem requires an isometry (rotation about a point, translation, reflection), students rotate the figure but forget to rotate the associated tangent line, axis or centre, so the transformed figure no longer satisfies the original condition.
The figure is treated as the only object of the transformation, while auxiliary elements (tangents, axes, centres of homothety) are left in their original position.
What to do instead
List every element of the construction that belongs to the moving set and transform all of them with the same isometry (same centre, same angle, same direction). After transforming, re-check the defining condition (e.g. the image circle must still be tangent to the fixed line) before inking the answer.