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Mensuration tells you how much a shape holds. Geometry tells you why the shape is what it is — and papers ask that second question far more often than students expect. Two to four marks in almost every general-mathematics section come from angle chasing, a right-triangle check, or a single circle property, and none of them need long calculation.
What makes geometry scoring is that the rules are finite. There are about a dozen results worth memorising, and every question is one of them wearing a disguise. A problem that looks like it needs construction usually needs the exterior-angle rule; one that looks like it needs trigonometry usually needs a Pythagorean triplet you already know.
Treat the next four cards as the rule sheet. Learn each statement, and more importantly learn the one situation it gets used in. A rule you can recite but cannot recognise inside a figure earns nothing in the exam hall.
1. In a triangle, one exterior angle measures 110° and one of its two interior opposite angles is 45°. The other interior opposite angle is:
2. The centroid of a triangle divides each median in the ratio (measured from the vertex to the opposite side):
3. A chord subtends an angle of 130° at the centre of a circle. The angle it subtends at any point on the major arc is:
4. Which of the following sets of lengths can form the sides of a right-angled triangle?
5. Two parallel lines are cut by a transversal. If one of the co-interior (allied) angles is 65°, the other co-interior angle is:
6. In a right-angled triangle, the circumcentre lies:
7. Two similar triangles have their corresponding sides in the ratio 3 : 5. The ratio of their areas is:
8. ABCD is a cyclic quadrilateral in which angle A = 105°. The measure of angle C is: