...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....

...respectively therefore, by property of proportional intercepts AD AE Result. 2 Conversely, if a line divides two sides of a triangle proportionally, it is parallel to the third side. Result. 3 Result 1 can be put in the following form in a AABC, a line DE in drawn parallel to BC and...

...other two sides proportionally. The converse theorem is also true, namely THEOREM 50. If a line divides two sides of a triangle proportionally, it is parallel to the third side. Note particularly that Th. 49 tells us nothing in fig. 17-1 about the XY ratio SJ. The proof of Th....

...other two sides proportionally. The converse theorem is also true, namely THEOREM 53. If a line divides two sides of a triangle proportionally, it is parallel to the third side. Ex. 3O. A variable line, drawn through a fixed point O, cuts two fixed parallel straight lines at P,...

...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;...