Triangles
Haryana Board · Class 10 · Mathematics
All formulas from Triangles in Haryana Board Class 10 Mathematics. Key equations, constants, and identities for board exam preparation.
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Basic Proportionality Theorem (BPT) — Thales Theorem
AD/DB = AE/EC
AD/AB = AE/AC = DE/BC
Criteria for Similarity of Triangles
△ABC ~ △DEF ⟺ ∠A=∠D, ∠B=∠E, ∠C=∠F AND AB/DE = BC/EF = CA/FD
AAA: ∠A=∠D, ∠B=∠E, ∠C=∠F ⟹ AB/DE = BC/EF = CA/FD
SSS: AB/DE = BC/EF = CA/FD ⟹ ∠A=∠D, ∠B=∠E, ∠C=∠F
SAS: AB/DE = AC/DF AND ∠A=∠D ⟹ △ABC ~ △DEF
RHS Similarity: Hyp₁/Hyp₂ = Side₁/Side₂ ⟹ △1 ~ △2
Key Theorems — Proof Techniques
ar(△ADE)/ar(△BDE) = AD/DB
ar(△ADE)/ar(△DEC) = AE/EC
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