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If a line divides two sides of a triangle proportionally, it is parallel to the third side.
A Text-book of Geometry - Page 136
by George Albert Wentworth - 1888 - 386 pages

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...AB — A'B', BC— B'C', etc. PROPOSITION II.— THEOREM. 19. Conversely, if a straight line divides two sides of a, triangle proportionally, it is parallel to the third side. Let DE divide the sides AB, AC, of the triangle ABC, proportionally; then, DE is parallel to BC. For,...

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...have AB = A'B', BC=B'C', etc. PROPOSITION II.— THEOREM. 19. Conversely, if a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Let DE divide the sides AB, AC, of the triangle ABC, proportionally; then, DE is parallel to £C. For,...

Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...one of the sides of a triangle, cuts the other sides proportionally ; and conversely, if a line cuts two sides of a triangle proportionally, it is parallel to the third side. This theorem may also be proved from LXXI., thus : — In Д А B С let DE be parallel to B С, then...

Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 376 pages
...FH. In like manner, we have, EG : GK :: FH : HL, and so on. PROPOSITION XII. THEOREM. If a line cuts two sides of a triangle proportionally it is parallel to the third side. Let EF cut the sides AD and CD, of the triangle ACD, so that AE : ED :: CF : FD; . . (1) then is EF...

Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...corresponding part. Now EB : AE : : FC : A F. §275 By composition, PROPOSITION III. THEOREM. 277. If a straight line divide two sides of a triangle proportionally, it is parallel to the third side. A In the triangle ABC let EF be drawn so that — = —. AE AF We are to prove EF II to B C. From E...

Elements of Geometry: And the First Principles of Modern Geometry

William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...PROVED. OA : Oa = OB : O& = OC : Oc = OD : Od. xvni. Theorem. Converse!y, if a straight line divides two sides of a triangle proportionally, it is parallel to the third side. HYPOTH. In the triangle ABC, AD : DB=AE : EC. To BE PROVED. The line DE [| BC. \ BOOK III.] PROPORTIONAL...

Elements of Geometry

George Albert Wentworth - 1881 - 266 pages
...EB + AE : AE : : FС+ AF : AF, §263 or, AB : AE : : A С : A F. PROPOSITION III. THEOREM. 277. If a straight line divide two sides of a triangle proportionally, it is parallel to the third side. A In the triangle ABC let EF be drawn so that =. We are to prove EF II to B С. From E draw EH II to...

Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1882 - 442 pages
...FC+AF : AF, §263 or, AB : AE : : AC : A F. 142 GEOMETRY. BOOK III. PROPOSITION III. THEOREM. 277. If a straight line divide two sides of a triangle proportionally, it is parallel to the'third tide. A In the triangle ABC let EF be drawn so żżat — = — . AE AF We are to prove EF...