Triangles · Mathematics, chapter 6
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Similar triangles and the Basic Proportionality Theorem
conceptId: similar-triangles
Similar triangles and the Basic Proportionality Theorem
CBSE Class 10 Mathematics · Ch 6 §6.3 — a line parallel to one side of a triangle divides the other two sides in the same ratio.
- AD / DB
- 1.0000
- AE / EC
- 1.0000
- DE / BC
- 0.5000
- AB / AD (similarity scale)
- 2.0000
- |m(DE) − m(BC)| (parallel ⇒ 0)
- 0.00e+0
- AD, DB, AE, EC
- 4.243 , 4.243 , 4.220 , 4.220
What to notice: slide D anywhere along AB and AD/DB keeps matching AE/EC — the Basic Proportionality Theorem. DE stays parallel to BC, and triangle ADE is just a scaled copy of triangle ABC by the factor AB/AD.
Try this: park D at the midpoint (t = 0.5) and check DE = BC/2. Then push t to 0.9 — AD/DB becomes 9 and AE/EC must still agree to four decimal places.
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