Proportionality theorem and its converse

Basic proportionality Theorem

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:

5. A B C D E N M Construction:

6. A B C D E N

7. A B C D E M

8. A B C D E

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:

11. A B C D E To prove:

12. A B C D E F Construction

13. A B C D E F

14. A B C D E

15. A B C D E

16. A B C D E Corollary 3

17. A B C AD/AB=AE/AC …….1 D E BF/BC=AE/AC DE/BC=AE/AC..2 F