Geometry Basics – Quick Study Notes
(For the Jammu & Kashmir Police Constable – Quantitative Aptitude)
1. Why Geometry?
- Geometry deals with shapes, sizes, and positions of objects.
- In everyday life we use it to measure rooms, plan routes, or calculate distances.
2. Basic Building Blocks
| Concept | Everyday Analogy | Quick Note |
|---|---|---|
| Point | A tiny dot on a map. | No size, just a location. |
| Line | A straight road. | Unlimited in both directions. |
| Segment | The stretch between two road signs. | Finite, has two endpoints. |
| Ray | A road that starts at a sign and goes on forever. | One endpoint, the rest extends infinitely. |
| Plane | A flat table. | Two‑dimensional surface. |
3. Angles – How Big is a Turn?
| Angle Type | Everyday Analogy | Key Feature |
|---|---|---|
| Right angle | A corner of a book. | Exactly 90°. |
| Acute angle | A sharp turn on a road. | Less than 90°. |
| Obtuse angle | A wide bend in a path. | More than 90° but less than 180°. |
| Straight angle | A straight road. | Exactly 180°. |
Tip: If you can lay a ruler flat on it, it’s a right angle.
4. Common Shapes & Their Names
| Shape | Everyday Example | What We Usually Measure |
|---|---|---|
| Triangle | A slice of pizza. | 3 sides, 3 angles. |
| Rectangle | A door frame. | Opposite sides equal. |
| Square | A chessboard square. | All sides equal, all angles 90°. |
| Circle | A coin. | No corners, one smooth edge. |
5. Perimeter – The “Walk Around” Length
- Perimeter = Total length of the outline.
- Think of walking along the edge of a shape.
| Shape | Perimeter Formula | Tiny Example |
|---|---|---|
| Rectangle | 2 × (Length + Breadth) |
A 4 m × 3 m room → 2 × (4 + 3) = 14 m. |
| Square | 4 × Side |
5 m side → 4 × 5 = 20 m. |
| Triangle | Side1 + Side2 + Side3 |
3 m + 4 m + 5 m = 12 m. |
| Circle | 2 × π × Radius |
Radius 2 m → 2 × 3.14 × 2 ≈ 12.56 m. |
Use π ≈ 3.14 for quick work.
6. Area – “How Much Floor”
- Area = Amount of flat space inside a shape.
- Think of covering the floor with tiles.
| Shape | Area Formula | Tiny Example |
|---|---|---|
| Rectangle | Length × Breadth |
4 m × 3 m = 12 m². |
| Square | Side × Side |
5 m × 5 m = 25 m². |
| Triangle | ½ × Base × Height |
Base 6 m, Height 4 m → ½ × 6 × 4 = 12 m². |
| Circle | π × Radius² |
Radius 2 m → 3.14 × 2² ≈ 12.56 m². |
7. Quick Practice Problems
| Problem | Simple Working |
|---|---|
| 1. A rectangular plot is 10 m long and 6 m wide. What is its perimeter? | 2 × (10 + 6) = 32 m. |
| 2. A square patch of land has a side of 7 m. Find its area. | 7 × 7 = 49 m². |
| 3. A circle has a radius of 3 m. Estimate its circumference. | 2 × 3.14 × 3 ≈ 18.84 m. |
| 4. A triangle with sides 3 m, 4 m, 5 m has what area? | ½ × 3 × 4 = 6 m². (Right‑triangle check). |
8. Handy Tips
- Remember π ≈ 3.14 – use it for quick circle calculations.
- Check units – meters (m) for lengths, square meters (m²) for areas.
- Use the “walk‑around” idea for perimeter; use “tile the floor” idea for area.
- Draw a quick sketch – even a rough line picture helps you see the shape.
9. One‑Minute Review
- Point, line, segment, ray, plane – the very first building blocks.
- Angles – right, acute, obtuse, straight.
- Shapes – triangle, rectangle, square, circle.
- Perimeter – walk around the shape.
- Area – cover the floor with tiles.
Keep practicing a few numbers each day, and you’ll master the basics in no time!