Geometry
Geometry in SEE Optional Mathematics tests deductive reasoning with triangle and circle theorems, properties of quadrilaterals, ruler-and-compass construction, and transformation of figures.
Triangles and quadrilaterals
Use congruence criteria (SSS, SAS, ASA, RHS) and similarity (AA, SSS, SAS). In a parallelogram, opposite sides and angles are equal and diagonals bisect each other; a rectangle has equal diagonals; a rhombus has perpendicular diagonals; a square combines both. The midpoint theorem: the segment joining midpoints of two sides is parallel to the third side and half its length.
Circles
The angle at the centre is twice the angle at the circumference standing on the same arc. Angles in the same segment are equal. A cyclic quadrilateral has opposite angles supplementary. The tangent at a point is perpendicular to the radius drawn to that point; tangents from an external point are equal. The alternate segment theorem relates the angle between a tangent and chord to the angle in the alternate segment.
Construction and transformation
Construction questions expect accurate arcs, labelled vertices, and a written statement of steps. Transformations: translation adds a vector, reflection uses a mirror line, rotation needs centre and angle, enlargement uses a scale factor from a centre. State the image coordinates clearly.
Worked example
In a cyclic quadrilateral ABCD, angle A=3x and angle C=x+40°. Opposite angles are supplementary: 3x+x+40=180, so 4x=140, x=35°. Then angle A=105° and angle C=75°.
Traps
Assuming a figure is cyclic without proof; using the tangent–radius theorem on a line that is not a tangent; giving construction steps without arcs; confusing enlargement with translation.