Chapter 6 · Class 10 CBSE · Formula Sheet
Triangles Formulas — Class 10 CBSE
Prove and apply BPT, similarity criteria, and Pythagoras theorem with proofs.
Key Formulas
Basic Proportionality Theorem (BPT)
\dfrac{AD}{DB} = \dfrac{AE}{EC}
If DE is parallel to BC in triangle ABC
AAA Similarity
\text{All three angles equal}
SAS Similarity
\text{Two sides proportional and included angle equal}
SSS Similarity
\text{All three sides proportional}
Area Ratio
\dfrac{\text{Area}(\triangle_1)}{\text{Area}(\triangle_2)} = \dfrac{a_1^2}{a_2^2}
Pythagoras Theorem
\text{Hypotenuse}^2 = \text{Base}^2 + \text{Perpendicular}^2
Worked Examples
1Using: Supplementary Angles
If one angle is 65 degrees, find its supplement.
Step 1: Supplement = 180 - 65
Step 2: = 115 degrees.
Answer: 115 degrees
2Using: Vertically Opposite
Two lines intersect. If one angle is 40 degrees, find the vertically opposite angle.
Step 1: Vertically opposite angles are equal.
Step 2: The angle = 40 degrees.
Answer: 40 degrees
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