Triangles — Notes
📑 Chapter Navigator
01
6.1 Similar Figures
Two figures are similar when they have the same shape, though their sizes may differ. Corresponding angles are equal and corresponding sides are proportional.
02
6.2 Basic Proportionality Theorem
If a line is drawn parallel to one side of a triangle and intersects the other two sides, it divides those sides in the same ratio.
Converse
If a line divides two sides of a triangle in the same ratio, then the line is parallel to the third side.
03
6.3 Similarity Criteria
Triangles are similar by AA, SSS or SAS similarity when the corresponding conditions are satisfied.
04
6.4 Areas of Similar Triangles
If two triangles are similar, the ratio of their areas equals the square of the ratio of corresponding sides:
Area₁/Area₂ = (corresponding side₁/corresponding side₂)2.
Area₁/Area₂ = (corresponding side₁/corresponding side₂)2.
05
6.5 Pythagoras Theorem
In a right triangle, hypotenuse2 = base2 + perpendicular2. Its converse can be used to establish whether a triangle is right-angled.
⚡ Quick Revision
- Parallel line inside triangle → proportional division.
- AA, SSS and SAS are similarity criteria.
- Area ratio of similar triangles is the square of side ratio.
- Pythagoras: c²=a²+b² in a right triangle.
🎯 Board Exam Focus
- Match corresponding vertices correctly.
- Do not use side ratio directly for area ratio; square it.
- Mention the theorem used in proof-based answers.
🚀 Last-Minute Revision
✔ Read every formula with its conditions and symbols.
✔ Write given data first and keep units consistent.
✔ For proofs, state the theorem and show logical steps.
✔ Check signs, substitutions and final units.
❤️ Examisthan.com • Class 10 CBSE Mathematics • Chapter 6: Triangles