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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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Information Relative to the Appointment and Admission of Cadets to the ...

Military Academy, West Point - 1934 - 964 pages
...polygon whose vertices are А, В, С, D,E. В X С X XX AE D X Г 10 Theorem: If n straight line divides two sides of a triangle proportionally, it is parallel to the third side. I 10 Problem: Inscribe a regular decagon In a given circle. I 10 Theorem: ADCD is given square. E,...
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Geometry - Plane, Solid and Analytic Problem Solver

Research & Education Association Editors, Ernest Woodward - Mathematics - 2012 - 1080 pages
...line parallel to one side of a triangle divides the other two sides proportionally. If a line divides two sides of a triangle proportionally, it is parallel to the third side. The bisector of one angle of a triangle divides the opposite side in the same ratio as the other two...
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Geometry I Essentials

The Editors of REA - Mathematics - 2013 - 112 pages
...A /\ If DE II BC, then / \ AD-AE D / _ \ F BD ~ CE ~/ NT Figure 8.1 e C Theorem 2 If a line divides two sides of a triangle proportionally, it is parallel to the third side. Theorem 3 The bisector of one angle of a triangle divides the opposite side in the same ratio as the...
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Composite Mathematics Book-8

S. K. Gupta & Anubhuti Gangal - Mathematics - 284 pages
...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...
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The New Geometry: Form One

G. P. West - Geometry - 1965 - 362 pages
...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....
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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 356 pages
...the given polygon, with AG as a side homologous to m. PROPOSITION IV. THEOREM 378. If a line divides two sides of a triangle proportionally, it is parallel to the third side. A —- A— G B Given the triangle ABC, and the line DE drawn so that AD AE &B~1$C' To prove that DE...
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Paractical Geometry Based on the Various Geometry Books by Godfrey and Siddons

480 pages
...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,...
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School Certificate Mathematics

Mathematics - 1965 - 232 pages
...PBQC' 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....
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Cambridge Intermediate Mathematics, Part 2

Herbert James Larcombe - 1928 - 272 pages
...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;...
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ICSE Mathematics Part 2 for Class X

646 pages
...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 ——...
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