 | Thomas Lund - Geometry - 1854 - 520 pages
...For / BEG = / AEF (31), .-. / AEF =/ EFD, and .'. AB, CD are parallel, as already proved. COR. 2. If the two interior angles on the same side of the intersecting line are together equal to two right angles, the two straight lines shall be parallel. For, since / BEF... | |
 | Richard Wormell - Geometry, Modern - 1868 - 286 pages
...alternate angles. 2nd. Of the exterior alternate angles. 3rd. Of the corresponding angles. 7. Prove that the sum of the two interior angles on the same side of the transversal is equal to two right-angles. 8. Prove that two angles are equal when their sides are parallel... | |
 | James Maurice Wilson - Geometry - 1868 - 132 pages
...same manner it may be shewn that any angle in the figure is equal to its corresponding angle. COR. 2. Of the two interior angles on the same side of the intersecting line, each is supplementary to the other. For FGD is supplementary to DGH (Th. 3. Cor. i), and therefore... | |
 | Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...Suppose the [_ FGB = [_ aHD. Adding the |_ S.aB to each, we have |_ FaB + L HG-B = L GHD + HaB. But the first member of this equation is equal to two right angles ; hence the second member is also equal to two right angles ; and by the theorem, the lines AB and... | |
 | Richard Wormell - Geometry, Plane - 1870 - 304 pages
...alternate angles. 2nd. Of the exterior alternate angles. 3rd. Of the corresponding angles. 7. Prove that the sum of the two interior angles on the same side of the transversal is equal to two right-angles. 8. Prove that two angles are equal when their sides are parallel... | |
 | 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. Scholium.... | |
 | 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 outside... | |
 | Edward Olney - 1872 - 270 pages
...data aiidthe 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 right angles ; and the conclusion is, that The two lines are parallel.... | |
 | 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. Scholium.... | |
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...queotion is applied moat directly. 1. If two straight lines are parallel, and a third, meets them, the two interior angles on the same side of the intersecting line are together equal to two right angles. The two lines AB and CD are parallel (ie, howE ever far they... | |
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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 secant line is equal to two right angles. 
