Geometry Basics – SSC JE (Quantitative Aptitude)
Aim – To give you a concise, quick‑reference guide for all geometry topics that appear in the SSC JE exam.
Format – Simple explanation → Key points (with formulas) → Worked example → Revision summary.
Tip – Keep a small notebook or a flash‑card with the formulas; practise 5–10 problems a day.
1. Simple Explanation
Geometry in SSC JE deals with figures (points, lines, angles, triangles, quadrilaterals, circles) and their measures (perimeter, area, length).
All questions are either pure geometry (no coordinates) or use simple coordinate geometry (distance, midpoint, area of triangle).
The key is to remember the standard formulas and the conditions under which they are valid.
2. Key Points
| Category | Concept | Formula / Property | Notes |
|---|---|---|---|
| Basic Elements | Point, Line, Plane | – | |
| Angles | Acute, Right, Obtuse | Sum in triangle = 180°; Sum in quadrilateral = 360° | |
| Triangles | Equilateral, Isosceles, Scalene | – | |
| Sum of internal angles | 180° | ||
| Pythagoras | (a^2+b^2=c^2) (right triangle) | ||
| Area (right triangle) | (\frac{1}{2}\times \text{leg}_1 \times \text{leg}_2) | ||
| Area (any triangle) | (\frac{1}{2}\times \text{base}\times \text{height}) | ||
| Altitude from a vertex | ( \text{height} = \frac{2 \times \text{Area}}{\text{base}}) | ||
| Heron’s formula | (\sqrt{s(s-a)(s-b)(s-c)}) where (s=\frac{a+b+c}{2}) | ||
| Circumradius (R) | (R = \frac{abc}{4\Delta}) | ||
| Inradius (r) | (r = \frac{2\Delta}{a+b+c}) | ||
| Congruence | SSS, SAS, ASA, AAS, HL (right triangle) | ||
| Similarity | SSS, SAS, AA | ||
| Quadrilaterals | Parallelogram | Opposite sides equal, diagonals bisect each other | |
| Rectangle | All angles 90°, opposite sides equal | ||
| Square | All sides equal, all angles 90° | ||
| Rhombus | All sides equal, diagonals perpendicular, bisect each other | ||
| Trapezium (US)/Trapezoid (UK) | One pair of parallel sides | ||
| Area of any quadrilateral | (\frac{1}{2}\times d_1 \times d_2) (if diagonals perpendicular) | ||
| Parallelogram area | (\text{Base}\times \text{Height}) | ||
| Circle | Radius (r) | – | |
| Diameter (D) | (D = 2r) | ||
| Circumference | (C = \pi D = 2\pi r) | ||
| Area | (A = \pi r^2) | ||
| Arc length | (L = \frac{\theta}{360}\times C) (θ in degrees) | ||
| Sector area | (A = \frac{\theta}{360}\times \pi r^2) | ||
| Chord length | (c = 2r \sin(\frac{\theta}{2})) | ||
| Tangent‑secant theorem | (t^2 = \text{product of secant segments}) | ||
| Coordinate Geometry | Distance between ((x_1,y_1)) and ((x_2,y_2)) | (d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}) | |
| Mid‑point | (\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)) | ||
| Area of triangle using coordinates | (\frac{1}{2}\left | x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right | |
| Slope of line | (m = \frac{y_2-y_1}{x_2-x_1}) | ||
| Parallel lines | Equal slopes | ||
| Perpendicular lines | Product of slopes = -1 |
Quick Formula Cheat‑Sheet
| Problem | Formula |
|---|---|
| Circumference of a circle | (C = \pi D) |
| Area of a circle | (A = \pi r^2) |
| Area of rectangle | (A = l \times w) |
| Area of parallelogram | (A = b \times h) |
| Area of triangle (right) | (A = \frac{1}{2}ab) |