← CBSE Class 10
Triangles
Chapter Overview
Two figures are similar if they have the same shape but not necessarily the same size. Triangles are similar if corresponding angles are equal and corresponding sides are proportional. The Basic Proportionality Theorem (Thales Theorem): if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides those sides in the same ratio. Criteria for similarity: AAA, SSS, and SAS similarity. The Pythagoras theorem: in a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides. Its converse is also true.
Topics Covered
- Similar Figures
- Similar Triangles
- Basic Proportionality Theorem
- Thales Theorem
- AAA Similarity
- SSS Similarity
- SAS Similarity
- Pythagoras Theorem
- Converse of Pythagoras
- Right Triangle Proofs
Key Formulas
If DE || BC, then AD/DB = AE/EC
AAA: A = D, B = E, C = F
SSS: AB/DE = BC/EF = CA/DF
SAS: AB/DE = BC/EF, B = E
AC2 = AB2 + BC2 (Pythagoras)
Real-World Applications
Applications: Surveying, map scaling, architecture, height measurement, navigation.
Study Tips
Tip: Learn the similarity criteria thoroughly
Tip: Practice applying Thales theorem in different figures
Tip: Master Pythagoras theorem proofs