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Basic proportionality Theorem

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- 1. PROPORTIONALITY THEOREM AND ITS CONVERSE
- 2. A B C D E Theorem : If a line is drawn parallel to one side of a triangle, then it divides other two sides proportionately
- 3. A B C D E Given:
- 4. A B C D E To prove: EC AE BD AD
- 5. A B C D E N M Construction:
- 6. A B C D E N NEADADEArea 2 1 NEBDBDEArea 2 1 1...... BD AD BDE ADE
- 7. A B C D E M DMAEADEArea 2 1 DMECCDEArea 2 1 2...... EC AE CDE ADE
- 8. A B C D E 2...... EC AE CDE ADE 1...... BD AD BDE ADE CDEBDE EC AE BD AD
- 9. Converse: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.
- 10. A B C D E Given: EC AE BD AD
- 11. A B C D E To prove:
- 12. A B C D E F Construction
- 13. A B C D E F 1......given EC AE BD AD 2...... EF AE BD AD EF AE EC AE From ,2&1 EFEC
- 14. A B C D E AE AC AD AB TPCorollary ..:2 AE CE AD BD 11 AE CE AD BD AE AECE AD ADBD AE AC AD AB
- 15. A B C D E EC AC DB AB Corollary :1 EC AE BD AD EC AC BD AB 11 EC AE BD AD EC ECAE BD BDAD
- 16. A B C D E Corollary 3 BC DE AC AE AB AD TP ..
- 17. A B C AD/AB=AE/AC …….1 D E BF/BC=AE/AC DE/BC=AE/AC..2 F

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