11
CBSE Marks
★★★★★
Difficulty
9
Topics
Very High
Board Weight
Topics Covered
9 key topics in this chapter
Similar Figures
Similarity of Triangles
Basic Proportionality Theorem (BPT)
Converse of BPT
Criteria for Similarity: AA, SAS, SSS
Proof of Pythagoras Theorem
Converse of Pythagoras Theorem
Areas of Similar Triangles
Ratio of Areas = Square of Ratio of Sides
Study Resources
Key Formulas
| Formula / Rule | Expression |
|---|---|
| BPT | \(AD/DB = AE/EC \text{ (if DE ∥ BC)}\) |
| AA Similarity | \(∠A = ∠D, ∠B = ∠E ⟹ △ABC ~ △DEF\) |
| Area Ratio | \(ar(△ABC)/ar(△DEF) = (AB/DE)^2\) |
| Pythagoras Theorem | \(BC^2 = AB^2 + AC^2 \text{ (right angle at A)}\) |
| Converse of Pythagoras | \(BC^2 = AB^2 + AC^2 \; \Rightarrow \; ∠A = 90°\) |
Important Points to Remember
BPT (Thales Theorem): A line parallel to one side of a triangle divides the other two sides proportionally.
Converse of BPT: If a line divides two sides of a triangle in the same ratio, it is parallel to the third side.
AA criterion: If two angles of one triangle equal two angles of another, the triangles are similar.
Ratio of areas of similar triangles = square of ratio of corresponding sides.