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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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Plane and Solid Geometry

Fletcher Durell - Geometry - 1911 - 553 pages
...QG~ A EQ AQ ''• QC EQ PROPOSITION XIV. THEOREM (CONVERSE OF PROP. 320. If a straight line divides two sides of a triangle proportionally, it is parallel to the third side. 23 C Given the A ABO and the line DF intersecting AB and AC so that AB : AD^AC : AF. To prove DF II...
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Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ...

International Correspondence Schools - Building - 1906 - 634 pages
...5), AB : AC = DB: EC In the same manner it may be shown that AB : AC = AD-.AE 11. If a line divides two sides of a triangle proportionally, it is parallel to the third side. Thus, if DE, Fig. 3, divides AB and AC so that AD : DB = AE: EC, then DEis parallel to B C. If DE were...
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Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...d = ih = i^(?) (305). "7 \ 4S All RS ^ AR RS ST PLANE GEOMETRY 307. THEOREM. 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 and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 440 pages
...DF : Also, AF : AG = DF : and AF : AG = FH : PROPOSITION XIV. THEOREM 343 If a straight line divides two sides of a triangle proportionally, it is parallel to the third side. HYPOTHESIS. In the A ABC, DE is so drawn that AB : AD = AC : AE. CONCLUSION. DE is || to BC. PROOF...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 431 pages
...AE = DF Also, AF : AG = DF and AF : AG = FH PROPOSITION XIV. THEOREM 343 If a straight line divides two sides of a triangle proportionally, it is parallel to the third side. HYPOTHESIS. In the A ABC, DE is so drawn that AB : AD = AC : AE. CONCLUSION. DE is || to BC. PROOF...
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Plane and Solid Geometry

Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...AGT, ^ = ^. (?) (305). AS ST . 'AC_=CE=EG Ax ^ AB RS ST PLANE GEOMETRY 307. THEOREM. 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 and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...the base of a triangle divides the other two sides proportionally. 341. If a straight line divides two sides of a triangle proportionally, it is parallel to the third side. 344. Mutually equiangular triangles are similar. 347. Triangles that have an angle in each equal, and...
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Wentworth's Plane Geometry

George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...across the upright piece; across the horizontal piece. PROPOSITION X. THEOREM 276. If a line divides two sides of a triangle proportionally, it is parallel to the third side. BO Given the triangle ABC with EF drawn so that EB _ FC ~AE~~AF' To prove that EF is II to BC. Proof....
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College Entrance Examination Papers in Plane Geometry

Geometry, Plane - 1911 - 192 pages
...angle formed by a tangent and a chord is measured by one-half the intercepted arc. 3. Demonstrate: If a straight line divide two sides of a triangle proportionally, it is parallel to the third side. 4. Construct: A parallelogram equivalent to a given square, and having the difference of its base and...
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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 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 Given the triangle ABC, and the line DE drawn so that AD AE DB~1SC To prove that DE II BC. Proof....
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