Parallel Lines സമാന്തരവരകൾ
How a set of parallel lines cuts every line that crosses them into equal parts, or into parts in a fixed ratio; how that lets you divide any line, build triangles and rectangles with a given perimeter, and prove the midpoint theorem; and how the medians and altitudes of a triangle always meet at one point. An interactive, animated self-study guide: the basics from earlier classes, every idea of the chapter with real-life uses, animated solutions to every textbook question, a revision sheet, and a model test with a fully solved paper.
How to use this guide
🎬 Watch the constructions
Every construction and proof is a step-by-step animation. Press Next ▶ to move one step at a time, or ▶▶ Auto play to watch it like a video. Keep your ruler, compass and set squares ready and draw along.
🖐️ Drag and slide
Orange dots can be dragged and sliders change lengths, ratios and angles. Watching the pieces stay equal (or stay in ratio) while you move things is the fastest way to feel why the theorems are true.
✍️ Try before you see
Questions come with a Show a hint button and a hidden final answer. Always attempt the question in your notebook first, then check. The quizzes give instant feedback.
📖 Textbook links
Purple മലയാളം words are the exact terms used in your textbook, so you can match every page here with the book (pages 33–60).
Learning path
Follow the pages in order. If you are confident with angles between parallel lines, congruent triangles and compass constructions, you may skim pages 1–4, but do try their quizzes.
The chapter in one picture
Lay a stick across the lines of a ruled notebook so that it reaches from one line to the n-th line below. The lines cut it into n equal pieces, whatever the tilt. Equally spaced parallel lines cut every line into equal parts – that single fact drives the whole chapter.
Quick glossary (Malayalam ↔ English)
| Textbook term | English | Meaning |
|---|---|---|
| സമാന്തരവരകൾ | Parallel lines | Lines in a plane that never meet; always the same distance apart |
| ലംബം | Perpendicular | A line at right angles (90°) to another |
| സമഭാഗം / അസമഭാഗങ്ങൾ | Equal parts / unequal parts | Division of a line into equal pieces / pieces in a ratio |
| അംശബന്ധം | Ratio | Comparison of two lengths, e.g. 2 : 3 |
| ചുറ്റളവ് / പരപ്പളവ് | Perimeter / area | Length around a figure / space inside it |
| മധ്യബിന്ദു | Midpoint | The point that halves a segment |
| സാമാന്തരികം / ലംബകം | Parallelogram / trapezium | Two pairs / one pair of parallel sides |
| ഉന്നതി | Altitude | Perpendicular from a vertex to the opposite side |
| നടുവര | Median | Line from a vertex to the midpoint of the opposite side |
| ലംബകേന്ദ്രം | Orthocentre | Where the three altitudes meet |
| മധ്യമകേന്ദ്രം | Centroid | Where the three medians meet; divides each median 2 : 1 |
| പരിവൃത്തകേന്ദ്രം | Circumcentre | Where the perpendicular bisectors of the sides meet |
| ഓയ്ലർ വര | Euler line | The line through the circumcentre, centroid and orthocentre |
Made for self-learning. Works offline – every page is a single file. Study material prepared by Claude for Madhu's family study folder, October 2026.