 | George Bruce Halsted - Geometry - 1886 - 394 pages
...z 499. COROLLARY I. If the points A and A' coincide, the figure ACC' will be a triangle ; therefore a line parallel to one side of a triangle divides the other two sides proportionally. 500. COROLLARY II. If two lines are cut by four parallel lines, the intercepts on the one are to one... | |
 | 1888 - 432 pages
...line drawn perpendicular to a radius at its extremity is tangent to the circle. Prove. 4. A line drawn parallel to one side of a triangle divides the other two sides proportionally. State and prove the converse proposition. 5. Show that the lines joining the middle points of adjacent... | |
 | George Albert Wentworth - 1889 - 276 pages
...lines, third proportional, mean proportional, extreme and mean ratio, segments of a line. 139. Theorem. A line parallel to one side of a triangle divides the other two sides into proportional parts ; and these two sides have the same ratio as two corresponding segments. 140.... | |
 | George Albert Wentworth - 1889 - 264 pages
...lines, third proportional, mean proportional, extreme and mean ratio, segments of a line. 139. Theorem. A line parallel to one side of a triangle divides the other two sides into proportional parts; and these two sides have the same ratio as two corresponding segments. 140.... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...portionally at P and Q if A " B AP : PB = CQ : QD. i ^ A Proposition 1 2. Theorem. 298. A straight line parallel to one side of a triangle divides the other two sides proportionally. Hyp. Let DB be || to BC in the A ABC. To prove AD : DB = AE : EC. CASE I. When AD and DB are commensurable.... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...parallel planes are cut by a third plane, the intersections are parallel.] (§ 417.) ' Therefore, [A parallel to one side of a triangle divides the other two sides proportionally.] (§ 245.) In like manner, = . (2) 17 /IN J /0\ From (1) and (2), DIEDRALS. DIEDRALS. DEFINITIONS. 426.... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...antecedents is to the sum of the consequents as any antecedent is to its consequent. 219. Theorem. A line parallel to one side of a triangle divides the other sides proportionally. 220. Theorem. A line which divides two sides of a triangle proportionally is... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...leads to an absurdity. 8. .--=- or-=-- Fund. prop. Ill PLANE GEOMETRY. D.\ \C. A./ /B. COROLLARIBS. 1. A line parallel to one side of a triangle divides the other two sides proportionally. For in the annexed figure, if BCD is the triangle, the lines OB, OC are cut by parallels. Hence BB1... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...one have the same ratio as the corresponding segments of the other. o.\ \c. C\\D /BCOROLLARIES. 1. A line parallel to one side of a triangle divides the other two sides proportionally. For in the annexed figure, if BCO is the triangle, the lines OB*, OC are cut by parallels. Hence BBi... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...DF=FH, etc. 'n trapezoid ABFE,' CD bisects one leg and is || to the bases PROPOSITION X 197. Theorem. A line parallel to one side of a triangle divides the other two sides proportionally. FIG. 1. FIG. 2. Case I (Fig. 1) Appl. When the side AB and its segment are commensurable. DE II BC... | |
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A line parallel to one side of a triangle divides the other two sides proportionally. 
