 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...remaining side and its corresponding segment. 157. Theorem HI. (Converse of Theo. II.) If a line divides two sides of a triangle proportionally, it is parallel to the third side. 160. Theorem IV. If two triangles have their homologous angles equal, the triangles are similar. 161.... | |
 | Alan Sanders - Geometry - 1903 - 396 pages
...the sides of the triangle. PROPOSITION XIV. THEOREM (CONVERSE OF PROP. XIII.) 474. // a line divides two sides of a triangle proportionally, it is parallel to the third side. Let — — — DB EC To Prove DE parallel to BC. Proof. Suppose DE is not parallel to BC and that... | |
 | 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... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...AQ' EQ AQ " QC EQ' PROPOSITION XIV. THEOREM (CONVERSE OF PROP. XIII) 320. // a straight line divides two sides of a triangle proportionally, it is parallel to the third side. BC Given the A ABC and the line DF intersecting AB and AC so that AB : AD=AC : AF. To prove DF \\ EC.... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...: AM = AF : AL = FIT : LM = HB:MN. §343 PROPOSITION XIV. THEOREM. 345. If a straight line divides two sides of a triangle proportionally, it is parallel to the third side. In the triangle ABC, let EF be drawn so that AB = AC AE AF' To prove that EF is II to BC. Proof. From... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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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If a line divides two sides of a triangle proportionally, it is parallel to the third side. 
