Chapter 24 · Class 11-12 & JEE Main/Adv
Properties of Triangle
28 topics in 14 parts
Angle Sum of a Triangle Sine Rule Cosine Rule for Side a Cosine Rule for Side b Cosine Rule for Side c Cosine of an Angle
Key ideas
Analytical Comparison & Distinction Matrix
| Analytical Method | Standard Representation | Parametric / Invariant Framework |
|---|---|---|
| Algebraic Nature | Explicit equations relating spatial coordinates | Parameterized using scalar parameters (λ, μ) or vectors |
| Symmetry Usage | Relies on coordinate expansion | Exploits vector dot/cross products for rapid simplification |
| Computational Efficiency | Direct for intercept evaluation | Superior for angles, orthogonal projections, and distances |
| Common Mistake | Sign confusion in determinants | Omitting boundary condition checks |
All 28 topics in Properties of Triangle
Standard Symbols
- Standard Symbols
Sine Rule
- Napier's Formula
Cosine Rule
- Cosine Rule
Projection Formula
- Projection Formula
Half-Angle Formulas
- Half-Angle Formulas
Area of Triangle
- Cevians & Area Ratios
Circles & Centers of a Triangle
- Centroid & Medians
- Circumcircle & Circumcenter
- Distances Between Triangle Centers
- Excircles & Excenters
- Incircle & Incenter
- Orthocenter & Altitudes
- Pedal Triangle
- Inradius & Circumradius Relations
Quadrilaterals & Polygons
- Area of Quadrilateral
- Cyclic Quadrilateral
- Incircles in Polygons
- Regular Polygons
- Triangle Inequality
Solution of Triangles
- Ambiguous Cases
- Similar Triangles
- Special Triangles
Napier's Analogy
- Napier's Analogy
m-n Theorem
- m-n Theorem
Sides in AP, GP & HP
- Sides in AP, GP & HP
Trigonometric Identities
- Trigonometric Identities
Heights & Distances
- Angles of Elevation & Depression
- Angles Subtended by Objects