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" If two parallel lines are cut by a transversal, the sum of the two interior angles on the same side of the transversal is two right angles. "
Plane Geometry: A Complete Course in the Elements of the Science - Page 48
by Edward Brooks - 1901 - 266 pages
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...sometimes called opposite exterior and interior angles. THEOREM XvII. If two straight lines are cut ly a third line, making the sum of the two interior angles on the same side equal to two right angles, the two lines will T)e parallel. For we have BGH + BGE = 2 right E angles...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 474 pages
...the direction of the lines, are sometimes called opposite exterior and interior angles. THEOREM XVH. If two straight lines are cut by a third line, making...the sum of the two interior angles on the same side equal to two right angles, the two lines will be parallel. For we have BGH + BGE = 2 right « angles...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 468 pages
...the same direction are parallel, (Def. 13). Hence the theorem ; if a line intersects two other lines, making the sum of the two interior angles on the same side of the intersecting line equal to two right angles, the two lines must be parallel. Cor. 1. If a line...
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An Elementary Course of Plane Geometry

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 and...
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Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...the same direction are parallel, (Def. 13). Hence the theorem ; if a line intersects two other lines, making the sum of the two interior angles on the same side of the intersecting line equal to two right angles, the two lines must b* •parallel. Cor. 1. If a line...
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An Elementary Course of Plane Geometry

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 and...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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....
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...scholium will save the student from confounding these propositions.] PROPOSITION T. 135. Theorem. — If two straight lines are cut by a third line making the sum of the interior angles on one side of the secant line less than two right angles, the /wo lines will meet...
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A Treatise on Special Or Elementary Geometry

Edward Olney - 1872 - 270 pages
...scholium will save the student from confounding these propositions.] PROPOSITION V. 155. Theorem.—If two straight lines are cut by a third line making the sum of the interior angles on one side of the secant line less than two right angles, the two lines will meet...
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Elements of geometry, with ... trigonometry

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...
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