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" If a line divides two sides of a triangle proportionally, it is parallel to the third side. "
Principles of Plane Geometry - Page 28
by James Wallace MacDonald - 1889 - 63 pages
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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,...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Mathematics - 1872 - 382 pages
...— 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, DEis parallel to BC. For,...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...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...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 412 pages
...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...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 426 pages
...: : F С : A F. 275 By composition, PROPOSITION III. THEOREM. 277. 1f a straight line divide two sides of a triangle proportionally, it is parallel to the third side. A la the triangle ABС let EF be drawn so that — = — . AE AF We are to prove EF II to B С. From...
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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...
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Elements of Geometry

George Albert Wentworth - 1881 - 266 pages
...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...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...like manner, EG : GB :: FH : HD; and so on. PROPOSITION XVI. THEOREM. // a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Let ABC be a triangle, and let DE divide AB and AC, so that AD : DB :: AE : EC; then DE is parallel...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 364 pages
...triangle divides the other two sides proportionally. PROPOSITION II. If a straight line divides two sides of a triangle proportionally, it is parallel to the third side. PROPOSITION III. • Two triangles are similar when they are mutually equiangular. PROPOSITION IV. Two triangles...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...(t>. 10), and also that PEOPOSITION II.— THEOREM. 15. 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,...
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