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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
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Robbin's New Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1915 - 280 pages
...(124). Hence AC : BD = CE : DF = EG : FH (Ax. 6). QED PROPOSITION XVI. THEOREM 296. If a line divides two sides of a triangle proportionally, it is parallel to the third side. Given: A ABC; line DE; the proportion AB : AC = AD : AE. To Prove : DE is II to BC. ^ Proof : Through...
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Plane Geometry

Jacob William Albert Young, Lambert Lincoln Jackson - Geometry, Plane - 1916 - 328 pages
...18 in., CF= 5 in., BE = 2 in. Find AD, AC, BC and GC. PROPOSITION VI. THEOREM 298. If a line divides two sides of a triangle proportionally, it is parallel to the third side. To prove that DE II AB. Proof. 1. If DE is not II AB, let the parallel to AB through D meet BC in F....
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Plane Geometry

Edith Long, William Charles Brenke - Geometry, Plane - 1916 - 292 pages
...other two sides proportionally. The converse of this theorem is: 214. Theorem XI. // a line divides two sides of a triangle proportionally, it is parallel to the third side. Given the triangle ABC with the line MN cutting the side AP AO AB&tP and side CA at Q, forming the...
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Plane and Solid Geometry

William Betz - Geometry - 1916 - 536 pages
...of a polygon similar to the given polygon, with AG as a side homologous to m. 378. If a line divides two sides of a triangle proportionally, it is parallel to the third side. B Given the triangle ABC, and the line DE drawn so that AD AE DB ~ EC To prove that DE II BC. Proof....
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Plane Geometry

John Charles Stone, James Franklin Millis - Geometry - 1916 - 298 pages
...meets AC at D and BC at E, then AC^BC , AC=BC AD BE DO EC. 124. Theorem. — If a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Hypothesis. In A ABC, DE meets AC at D and BC at E, , ,, . DC EC such that— = — Conclusion. DE...
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Plane Geometry

Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...other two sides proportionally. The converse of this theorem is: 214. Theorem XI. // a line divides two sides of a triangle proportionally, it is parallel to the third side. Given the triangle ABC with the line MN cutting the side AP AO AB at P and side CA atQ, forming the...
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Plane Geometry, with Problems and Application

Herbert Ellsworth Slaught - 1918 - 344 pages
...proportional to a and b. PROPORTIONAL DIVISION OF SIDES OF A TRIANGLE 330. THEOREM IV. If a line divides two sides of a triangle proportionally, it is parallel to the third side. A . B Given A ABC with points D and E on AC and EC such that CD = CE DA EB. To prove that DE II AB....
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1918 - 360 pages
...proportional to a and b. PROPORTIONAL DIVISION OF SIDES OF A TRIANGLE 330. THEOREM IV. If a line divides two sides of a triangle proportionally, it is parallel to the third side. ''••' ^E' AB Given A ABC with points D and E on AC and BC such that DA = EB' To prove that DE II...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...AB :AC=: m : n, •en ro and n are two given lines. PROPOSITION XVI. THEOREM 300. If a line divides two sides of a triangle proportionally, it is parallel to the third side. Given in A AEC, AB: BC=AD: DE. To prove DB parallel to EC. Proof. Through C, draw CE' parallel to BD,...
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Bulletin

Education - 1921 - 1190 pages
...a triangle parallel to the third side, it divides these sides proportionally. (b) If a line divides two sides of a triangle proportionally, it is parallel to the third side. (Proofs for commensurable cases only.) (c) The segments cut off on two transversals by a series of...
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