 | Timothy Walker - 1829 - 156 σελίδες
...equal to the fame thing are equal to each other. 35 . THEOREM. When two parallels are crossed by a straight line, the sum of the two interior angles on the same side is equal to two rig/it angles. If two parallel F 21 straight lines AB and CD (fig. 21) meet a third... | |
 | Nicholas Tillinghast - 1844 - 110 σελίδες
...will pursue the same direction as BA ; and hence the angle DEF is equal to ABC. PROP. IX. THEOREM. If two parallel lines are cut by a third straight line, the alternate angles will be equal. Fig. 9. E Let the parallels AB, CD, be cut by A the line EF ; then... | |
 | 1857 - 894 σελίδες
...parallel. For the proof, see Legendre's Geometry. THEOREM 2. — If two parallel straight lines meet a third straight line, the sum of the two interior angles on the same side must be equal to tioo right angles. Let the parallels AC and BD meet the line AN ; then BAC + ABD =... | |
 | George Roberts Perkins - 1856 - 460 σελίδες
...lines have the same direction, and are therefore parallel. THEOREM If two parallels are cut ly a third line, the sum of the two interior angles on the same side is equal to two right angles. Since the lines are parallel they E have the same direction, and their... | |
 | Horatio Nelson Robinson - 1860 - 470 σελίδες
...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... | |
 | George Roberts Perkins - 1860 - 472 σελίδες
...have the same direction, and are therefore parallel. THEOREM XVHI. If two parallels are cut by a third line, the sum of the two interior angles on the same side is equal to two right an./lex. Since the lines are parallel they K have the same direction, and their... | |
 | Richard Wormell - 1868 - 286 σελίδες
...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... | |
 | Richard Wormell - 1870 - 304 σελίδες
...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... | |
 | William Chauvenet - 1871 - 380 σελίδες
...are equal, the two lines are parallel. z 56. Corollary II. If the sum of the two interior angles DD the same side of the secant line is equal to two right angles, ;he two lines are parallel. 57. Corollary III. From (52) and (56) it follows that, when two straight... | |
 | William Chauvenet - 1871 - 380 σελίδες
...it, are called corresponding angles; as 1, 5—2, 6—3, 7—4, 8. PROPOSITION XIII.— THEOREM. 49. If two parallel lines are cut by a third straight line, the alternateinterior angles are equal. Let the parallels AB, CD, be cut by the straight line EF in 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 secant line is equal to two right angles. 
