Geometry Cheat Sheet
31 Oct 2026
Quick answer
A quick revision cheat sheet on geometry for SSC, Banking, Railway and state exams. It covers lines and angles, the triangle angle properties and Pythagoras theorem, the types of triangles, the interior and exterior angles of polygons, and the key circle angle rules, in a form you can revise quickly before the exam.
Geometry Cheat Sheet
Quick Revision
Geometry questions test the properties of angles, triangles, polygons and circles. Most answers come from a handful of angle and side rules.
Ready to practise? Take the Geometry quiz
1. Lines and Angles
| Pair of angles | Property |
|---|---|
| Complementary angles | Add up to 90° |
| Supplementary angles | Add up to 180° |
| Angles on a straight line | Add up to 180° |
| Angles around a point | Add up to 360° |
| Vertically opposite angles | Equal |
When a transversal cuts two parallel lines, corresponding angles are equal and alternate angles are equal.
2. Triangles
- The three interior angles add up to 180°.
- An exterior angle equals the sum of the two opposite interior angles.
- The sum of any two sides is greater than the third side.
| Type | Property |
|---|---|
| Equilateral | All sides equal; each angle 60° |
| Isosceles | Two sides equal; base angles equal |
| Scalene | All sides different |
| Right-angled | One angle is 90° |
Pythagoras theorem (right-angled triangle): hypotenuse² = base² + perpendicular².
3. Polygons
For a polygon with n sides:
Sum of interior angles = (n − 2) × 180°
Sum of exterior angles = 360° (always)For a regular polygon (all angles equal):
Each exterior angle = 360° / n
Each interior angle = 180° − (360° / n)Example
A regular hexagon (n = 6):
Each exterior angle = 360 / 6 = 60°
Each interior angle = 180 − 60 = 120°4. Circles
- The angle in a semicircle is 90°.
- The angle at the centre is twice the angle at the circumference on the same arc.
- Angles in the same segment are equal.
- A tangent meets the radius at the point of contact at 90°.
- Equal chords are equidistant from the centre.
5. Exam Quick Tips
- The three angles of a triangle sum to 180° — the most used rule.
- Exterior angle = sum of the two opposite interior angles.
- Interior-angle sum of a polygon is
(n−2)×180°; exterior-angle sum is always 360°. - In a circle, the angle in a semicircle is 90°.
Keep revising with the rest of the Maths section:
How this was made: Drafted with AI assistance; spot-checked by the editor on 31 October 2026.