Plane geometry: triangles, quadrilaterals and regular polygons
Plane geometry opens the Andalusian Technical Drawing II paper and feeds every later block, because solids are only drawn once their faces are built in true size. What is marked is the construction - compass and straightedge, auxiliary arcs left visible - not a measured result.
Triangles
Three independent data fix a triangle: three sides (arcs from the ends of one side), two sides and the included angle, one side and two adjacent angles, or two sides and an angle opposite one of them. The last case is the ambiguous one and may give two, one or no solutions. Know the notable points: circumcentre (perpendicular bisectors), incentre (angle bisectors), orthocentre (altitudes), barycentre (medians, at 2:1 from the vertex) and the Euler line carrying three of them. In a right triangle the altitude on the hypotenuse satisfies h² = m·n, and each leg is the mean proportional between the hypotenuse and its adjacent projection.
Quadrilaterals
A square is built from its side (perpendicular plus arcs of the side length) or from its diagonal (diagonal = s√2, the other diagonal being the perpendicular bisector). A rectangle needs a side and its diagonal; a rhombus a side and a diagonal; a parallelogram two sides and the angle or a diagonal; a trapezoid its bases, height and one side. A quadrilateral is cyclic when opposite angles sum 180°, and circumscribable when the sums of opposite sides are equal.
Regular polygons
Given the circumradius, divide the circle into n equal parts (central angle 360°/n) or apply the general method that divides a diameter into n parts by Thales. Given the side, the general method uses a semicircle on the extended side, divided into n parts, from which the centre of the circumcircle is obtained. Fast cases: hexagon side = radius; pentagon diagonal = φ·side (φ ≈ 1.618); octagon from the square of the radius.
Worked example
Regular pentagon of side AB = 40 mm. Erect a perpendicular at B of length 40, take the midpoint N of AB, and with centre the top of that perpendicular and radius to N cut AB produced at D; AD is the diagonal, about 64.7 mm. Arcs of radius AD from A and from B give the vertex opposite AB; arcs of radius 40 and radius AD complete the remaining two vertices.
Traps
Drawing only the final figure, with no construction arcs, loses most of the marks; stopping at the first solution of the ambiguous case; swapping apothem and radius when the polygon is given by its side; letting the compass opening drift between the two mirror solutions.