 | Webster Wells - 1886 - 392 strani
...bisects two of its angles, it is perpendicular to the other diagonal. 4. If two lines are cut by a third so as to make the sum of the interior angles on the same side of the secant line less than two right angles, the lines will meet if sufficiently produced. 6. If exterior... | |
 | Andrew Wheeler Phillips, Irving Fisher - 1896 - 276 strani
...parallel. Av. 7 . / n /a'" 7 Hint. — Reduce to Proposition X. by means of Proposition V. 45. COR. II. If two straight lines are cut by a third straight line so that the alternate-exterior angles are equal, the lines are parallel. Hint. — Reduce to Proposition... | |
 | Andrew Wheeler Phillips, Irving Fisher - 1896 - 276 strani
...are parallel. AY« 77 / a Hint. — Reduce to Proposition X.. by means of Proposition V. 45. COR. II. If two straight lines are cut by a third straight line so that the alternate-exterior angles are equal, the lines are parallel. Hint. — Reduce to Proposition... | |
 | Joseph Johnston Hardy - 1897 - 398 strani
...parallel straight lines are cut by a third straight line, the exterior interior angles are equal. 9. When two straight lines are cut by a third straight line, so as to make the exterior interior angles equal, these two straight lines are parallel. т0. Two straight lines which... | |
 | Webster Wells - 1898 - 264 strani
...BGH= Z CHG, and the theorem follows by § 40.) 76. Cor. II. If two parallels are cut by a transversal, the sum of the interior angles on the same side of the transversal is equal to two riyht angles. (Fig. of Prop. XXI.) Given IIs AB and CD cut by transversal EF at points... | |
 | Webster Wells - 1899 - 450 strani
...equal, AB II CD ? 79. Cor. II. (Converse of § 76.) If two straight lines are cut by a transversal, and the sum of the interior angles on the same side of the transversal is equal to two right angles, the two lines are parallel. (Fig. of Prop. XXII.) Given lines AB and... | |
 | Webster Wells - 1899 - 424 strani
...BGH= Z CHG, and the theorem follows by § 40.) 76. Cor. II. If two parallels are cut by a transversal, the sum of the interior angles on the same side of the transversal is equal to two right angles. (Fig. of Prop. XXI.) Given IIs AH and CD cut by transversal EF at points... | |
 | John Alton Avery - 1903 - 136 strani
...alternate-exterior anyles are equal. THEOREM XVIII 55. If two parallel lines are cut by a transversal, the sum of the interior angles on the same side of the transversal equals two right angles. NOTE. See figure for Theo. XVII. Hyp. See hyp. under Theo. XVI. To prove that... | |
 | Joseph Battell - 1903 - 722 strani
...third so that corresponding angles are equal, the straight lines are parallel. ' COROLLARY II. — If two straight lines are cut by a third straight line so that the alternate exterior angles are equal, the lines are parallel. PROPOSITION XI. 'If two parallel... | |
 | Arthur Wesley Chase - 1904 - 200 strani
...angles are equal. The converse or opposite of the foregoing statement is also true, that is to say : if two straight lines are cut by a third straight line so as to make the alternate interior angles equal, the two lines are parallel. The solution of this problem depends upon... | |
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... concerned with teaching than with learning, at all times. No doubt some of the geometries still teach as a self-evident truth the proposition that if two straight lines in one plane meet a third straight line so as to make the sum of the internal... 
