 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...other, tht. vertical angles must be equal. THEOREM V. If a straight line intersects two parallel lines, the sum of the two interior angles on the same side of the intersecting line is equal to two right angles. [NOTE. — By interior angles, we mean angles which... | |
 | Theophilus Parsons - History - 1861 - 500 pages
...angles are equal, the exterior angle and the interior opposite angle on the same side are equal, and that the sum of the two interior angles on the same side is equal to two right angles. I will now demonstrate that, when the two alternate angles are equal,... | |
 | Richard Wormell - Geometry, Modern - 1868 - 286 pages
...straight lines, that two straight lines perpendicular to a third are 1. Define i 2. Prove th parallel. 3. Every straight line perpendicular to one of two...parallel and directed the same way from the vertex. g. Two parallel lines are at the same distance from one another throughout. Explain the use and construction... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...corresponding angle. Thus, since HGB = GHC and GHC =FHD, there follows H GB = FHD; etc. 52. Corollary III. The sum of the two interior angles on the same side of the secant line is equal to two right angles. For, GHD -(HGB = GHD + GHC = two right angles (11). 53.... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...or data and the conclusions or things proved are exchanged. Thus, in PROP. III., the hypothesis is, that The sum of the two interior angles on the same side of the secant line is equal to two rigid angles ; and the conclusion is, that Tide two lines are parallel.... | |
 | André Darré - 1872 - 226 pages
...equal straight lines can be drawn to the circumference. 5. When a secant meets two straight lines, if the sum of the two interior angles on the same side of the secant is equal to two right angles, the lines are parallel. 6. To draw a line from a given point... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...corresponding angle. Thus, since HGB = GHC and GHC =FHD, there follows HGB = FHD; etc. 52. Corollary III. The sum of the two interior angles on the same side of the secant line is equal to two right angles. For, GHD -fHGB = GHD + GHC = two right angles (11). 53.... | |
 | Edward Olney - Geometry - 1877 - 272 pages
...parallel. Now, in PROP. IV., the hypothesis is, that The two lines are parallel; and the conclusion is, that The sum of the two interior angles on the same side of the secant line is two right angles.* [A. clear conception of this scholium will save the student from... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...PARALLEL LINES. PROPOSITION XV. THEOREM. 73. If two parallel lines be cut by a third straight line, the sum of the two interior angles on the same side of I lie secant line is equal to two right angles. B D Let AB and CD be two parallel lines cut by the... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...is II to CD. QED PROPOSITION XV. THEOREM. 73. If two parallel lines be cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles. D F Let AB and С D be two parallel lines cut by the... | |
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If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the transversal is equal to two right angles, (p. 
