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# Proportionality theorem and its converse

Basic proportionality Theorem

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### Proportionality theorem and its converse

1. 1. PROPORTIONALITY THEOREM AND ITS CONVERSE
2. 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. 3. A B C D E Given:
4. 4. A B C D E To prove: EC AE BD AD 
5. 5. A B C D E N M Construction:
6. 6. A B C D E N NEADADEArea  2 1 NEBDBDEArea  2 1 1...... BD AD BDE ADE   
7. 7. A B C D E M DMAEADEArea  2 1 DMECCDEArea  2 1 2...... EC AE CDE ADE   
8. 8. A B C D E 2...... EC AE CDE ADE    1...... BD AD BDE ADE    CDEBDE  EC AE BD AD 
9. 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. 10. A B C D E Given: EC AE BD AD 
11. 11. A B C D E To prove:
12. 12. A B C D E F Construction
13. 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. 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. 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. 16. A B C D E Corollary 3 BC DE AC AE AB AD TP ..
17. 17. A B C AD/AB=AE/AC …….1 D E BF/BC=AE/AC DE/BC=AE/AC..2 F