 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...point, C, so that AB:AC = m:n, when m and n are two given lines. i PROPOSITION XVI. THEOREM p 286. If a line divides two sides of a triangle proportionally, it is parallel to the third side. -V Hyp. In A AEC, AB:BC=AD: DE. To prove, DB parallel to EC. Proof. Through C, draw CE' parallel to... | |
 | Arthur Schultze - 1901 - 260 pages
...find a point, C, so that AB:AC=m:n, when TO and n are two given lines. PROPOSITION XVI. THEOREM 286. If a line divides two sides of a triangle proportionally, it is parallel to the third side. /\ .-- Hyp. In A AEC, AB:BC=AD: DE. To prove, DB parallel to EC. Proof. Through C, draw CE' parallel... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...point, C, so that AB:AC= TO:«, when m and n are two given lines. • PROPOSITION XVI. THEOREM 286. If a line divides two sides of a triangle proportionally, it is parallel to the third side. Hyp. In A AEC, AB : BC = AD : DE. To prove, DB parallel to EC. Proof. Through C, draw CE' parallel... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...principle established in this proposition. PROPOSITION XIV. THEOREM (CONVERSE OF PROP. XIII.) 474. If a line divides two sides of a triangle proportionally, it is parallel to the third side. B Let — — — DB ~ EC To Prove DE parallel to BC. Proof. Suppose DE is not parallel to BC and that... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...find a point, C, so that AB:AC= m:n, when m and n are two given lines. PROPOSITION XVI. THEOREM 286. If a line divides two sides of a triangle proportionally, it is parallel to the third side. Hyp. In A AEC, AB : BC = AD : DE. To prove, DB parallel to EC. Proof. Through C, draw CE' parallel... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...principle established in this proposition. PROPOSITION XIV. THEOREM (CONVERSE OF PROP. XIII.) 474. // a line divides two sides of a triangle proportionally, it is parallel to the third side. T . AD AE Let = —. DB EC To Prove DE parallel to BC. Proof. Suppose DE is not parallel to BC and... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...incommensurable case; but the above method seems preferable. PROPOSITION XVII. — THEOREM. CONVERSELY: // a line divides two sides of a triangle proportionally, it is parallel to the third side. To Prove. — Then we are to prove that DE is parallel to BC. Proof. — Suppose DE' drawn parallel... | |
 | James Howard Gore - Geometry - 1902 - 266 pages
...: EC, and (by 202), AB : AC = DB : EC. EXERCISES. 0 A 1. Conversely, if a straight line divides j \ two sides of a triangle proportionally, it is / \ parallel to the third side. / \ 2. If two straight lines AB, CD are cut EI \ f by any number of parallels, AC, EF, 0H, 7 V BD,... | |
 | Alan Sanders - Geometry - 1903 - 392 pages
...using the principle established in this and PROPOSITION XIV. THEOREM (CONVERSE OF PROP. XIII.) 474. If a line divides two sides of a triangle proportionally, it is parallel to the third side. B' Let A». = **. DB EC To Prove DE parallel to BC. Proof. Suppose DE is not parallel to BC and that... | |
 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...between the other 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.... | |
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If a line divides two sides of a triangle proportionally, it is parallel to the third side. 
