 | Arthur Schultze - Mathematics - 1912 - 398 pages
...measure, etc. To illustrate the use of this arithmetical plan further let us consider the theorem, A line parallel to one side of a triangle divides the other two proportionally. if AB is divided into five equal parts, then AD equals two of these parts. If through... | |
 | William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 134 pages
...proportion by alternation. 338. In any proportion like powers of the terms are in proportion. 340. A line parallel to one side of a triangle divides the other sides proportionally. 343. If a straight line parallel to the side BC of a triangle ABC cuts AB at... | |
 | Great Britain. Board of Education - Education - 1912 - 1044 pages
...find the angles which the smaller circle subtends at these points. 10. Show that a straight line drawn parallel to one side of a triangle divides the other two sides proportionally. AB is a straight line bisected at C ; an equilateral triangle ABD is described on AB,... | |
 | Great Britain. Board of Education - Mathematics - 1912 - 632 pages
...find the angles which the smaller circle subtends at these points. 10. Show that a straight line drawn parallel to one side of a triangle divides the other two sides proportionally. AB is a straight line bisected at C ; an equilateral triangle ABD is described on AB,... | |
 | William Benjamin Fite - Algebra - 1913 - 304 pages
...a vertical rod 5 feet long casts a shadow 4 feet long. How high is the tree ? 15. If a man 5 feet G inches tall casts a shadow 25 inches long, how high...similar to the original triangle. Thus in the figure - — = DB EC 16. If .4.8 = 20, AC =18, and AD = 14, how long are AE and EC? Hint. — Let x = length... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...externally. .. ,,—^_ t The segments of AB are AC and ACB PROPORTIONAL LINES PROPOSITION XIII. THEOREM* 293. A line parallel to one side of a triangle divides the other two sides proportionally. Given in A ABC, DE parallel to BC. To prove AD : DB = AB : EC. Proof.t CASE I. —... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...and ACB BC. The segments of A'B' are A' C' ( — PROPORTIONAL LINES PROPOSITION XIII. THEOREM * 293. A line parallel to one side of a triangle divides the other two sides proportionally. Given in A ABC, DE parallel to BC. To prove AD : DB = AE : EC. Proof, t CASE I. —... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 320 pages
...applications. They are stated as a theorem and proved in the following article. 192 411. Theorem. A straight line parallel to one side of a triangle divides the other two sides in the same ratio. Given AABC, having DE II AC. in j* To prove — = -, where m=AD, ns n=DB, r=CE,... | |
 | Webster Wells, Walter Wilson Hart - Geometry, Plane - 1915 - 330 pages
...— ~ - are variables which are always Z AOB arc AB equal. 8. ZAOB PROPOSITION XVII. THEOREM 424. A parallel to one side of a triangle divides the other two sides proportionally, when the segments of one side are incommensurable. A. Hypothesis. In A ABC, segments... | |
 | Ernst Rudolph Breslich - Mathematics - 1916 - 392 pages
...w, 9 " = Why? 0. .. . CD CE DA EB Similarly, we may prove (Tj = £5 ' CA = ' EXERCISES • 1. Prove that a line parallel to one side of a triangle divides the other two sides proportionally. (Apply § 163.) J2. Prove the theorem* in § 163, using Fig. 73. 164. Commensurable... | |
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A line parallel to one side of a triangle divides the other two sides proportionally. 
