Explore the properties of shapes, lines, and angles
Geometry is the study of shapes, sizes, and properties of figures and spaces. This section covers analytical geometry (coordinate geometry of lines) and trigonometry. Each topic includes interactive games and quizzes to test your understanding.
Select a topic to begin your studies.
| Topic | Formula | Description |
|---|---|---|
| Distance | d = √[(x2-x1)² + (y2-y1)²] | Distance between two points |
| Midpoint | M = [(x1+x2)/2, (y1+y2)/2] | Midpoint of line segment |
| Gradient | m = (y2-y1)/(x2-x1) | Slope of a line |
| Line Equation | y = mx + c | Slope-intercept form |
| Trig Ratios | sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adj | Right-angled triangle ratios |
Test your understanding of geometry before diving into the topics.
Hint: Recall the correct distance formula.
Use this Geometry section to practise both calculation and reasoning. Analytical geometry needs coordinates, gradients, midpoints, and distances, while Euclidean geometry needs clear diagrams, correct reasons, and logical proof steps.
For every geometry problem, redraw the diagram if needed, mark the given information, and write reasons beside your statements so your working is easy to follow.
A useful path from this page is to begin with Analytical Geometry, continue with Euclidean Geometry, and then test your understanding with Back to Mathematics. Do not rush through the links; spend time on the examples and make sure you can explain the main idea without looking at the notes.
Use this page to build definitions, worked examples, formulas, diagrams, and problem-solving methods. Write down key terms, formulas, diagrams, or steps that appear often so that revision becomes active instead of just rereading.
Keep a correction book for sign errors, formula mistakes, geometry reasons, and questions that need more practice. After each lesson, close the page and try a short self-test from memory before checking your notes again.
If you are stuck, start with algebra basics and number skills, because many later topics depend on accurate manipulation and clear working. If a topic feels too difficult, return to the previous link, revise the basics, and then try the examples again before using past papers.
