Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Proportionality theorem and its converse

Basic proportionality Theorem

  • Be the first to comment

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

×