 | Edward Olney - Geometry - 1872 - 472 pages
...not adjacent, as 2 and 0, 4 and 8, 1 and 5, 3 and 7. F1o. 123. PROPOSITION III. 147. Theorem. — If two lines are cut by a third line, making the sum of the interior anales on the same side of the secant line .equal lo two right angles, the two lines are parallel.... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...the four obtuse angles. PROPOSITION XXI. THEOREM. ' If two straight lines intersect a third straight line, making the sum of the interior angles on the same side less than two right angles, the two lines will meet if sufficiently produced. Let the two lines CD,... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...exterior and interior angles. PROPOSITION XIX. THEOREM. If two straight lines meet a third straight line, making the sum of the interior angles on the same side equal to two right angles, the two lines will be parallel. Let the lines KG and IID meet the line HA,... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...Proposition XI.— Theorem. If a straight line intersect two straight lines lying in tlie same plane, making the sum of the interior angles on the same side of the secant equal to two right angles, the two lines are parallel. Let EF intersect AB and CD, lying in the same... | |
 | Edward Olney - Geometry - 1877 - 272 pages
...the secant line but not adjacent, as 2 and 6, 4 and 8, 1 and 5, 3 and 7. V / PROPOSITION III. 147. Theorem.—If two lines are cut by a third line, making...the middle of CK, draw HI perpendicular to AB. Since HPC and KPI are vertical angles, they are equal by (1X4). Also, since CKB and CCK are both supplements... | |
 | Edward Olney - Geometry - 1879 - 502 pages
...and 5, 3 and 7. PROPOSITION in. 147. TJieorem. — If two lines are cvt by a third line, making te sum of the interior angles on the same side of the secant line nial to two right angles, the two lines are parallel DEM.— Let AB and CD be met by the line EF, making... | |
 | Edward Olney - 1879 - 278 pages
...Fia. 126. PROPOSITION IV. 15O. Theorem. — If two parallel lines are cut by a third line, tJie'sum of the interior angles on the same side of the secant line is equal to two right angles. DEM. — Let the parallels AB and CD be cut by EF, then is DCK + CKB... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...third line — I. The corresponding angles are equal; II. The alternate interior angles are equal; III. The sum of the interior angles on the same side of the secant equals two right angles. Let the IIs AB and CD be cut by the line EF. E Q fA D 0 d/P IJ F I. To prove... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...exterior and interior angles. PROPOSITION XIX. THEOREM. // two straight lines meet a third straight line, making the sum of the interior angles on the same side equal to two right angles, the t1ro lines are parallel. Let the lines KC and HD meet the line BA, making... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...= h and b = g. II. Any angle is equal to its corresponding angle ; that is, a = e, b = /, etc. III. The sum of the interior angles on the same side of the secant line is equal to two right angles ; that is, c + e = 180°, andd+/=180°. PROPOSITION XIII. THEOREM. 56.... | |
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If two lines are cut by a third, and the sum of the interior angles on the same side of the cutting line is less than two right angles, the lines will meet on that side when sufficiently produced. 
