...PB°QC' PROPORTIONAL DIVISION OF TWO LINES Theorem 34. (Converse of Theorem 33.) If a line divides two sides of a triangle proportionally, it is parallel to the third side. B Q C Given. P and Q are points on the sides AB, AC of A ABC such AP AQ Reqd. To prove PQ \\ BC. Proof....

...to a side of a triangle, it cuts the other sides proportionally. 2. If a line is drawn so as to cut two sides of a triangle proportionally, it is parallel to the third side. 9. Worked Examples, Ex. 1. D and E are points of trisection of the sides AB, AC of a triangle ABC;...

...Statements (1), (2) and (3). 1. (ii) Converse of the Basic Proportionality Theorem If a straight line cuts two sides of a triangle proportionally, it is parallel to the third side. A B C AP AQ Given : A straight lien PQ cuts AB and AC {produced in (ii)} in the same ratio ie ——...