...line, then 1. The alternate-interior angles are equal. ®. The exterior-interior angles are equal. 3. The sum of the interior angles on the same side of the transversal is equal to two riglit angles. UG HN Given — AB and CD parallel and cut by EF. To Prove, 1st — Z c = Z 6. Dem....

...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 directed the same...

...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 directed the same...

...THEOREM. < 109. If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the transversal is equal to two right angles. -B -D Let AS and CD be two parallel lines cut by the straight line EF in the points H and K. To prove...

...pioneers in the non-euclidean field. Euclid assumed as axiomatic, that, "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...

...parallel. 109. If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the transversal is equal to two right angles. 110. When two straight lines are cut by a third straight line, if the two interior angles on the same...

...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 G and H, respectively....

...from the sides of the angle. (Prove by Reductio ad Absurdum.) '. 2. If two lines are cut by a third, and the sum of the interior angles on the same side of the transversal is less than two right angles, the lines will meet if sufficiently produced. (Prove by Reductio ad Absurdum.)...

...from the sides of the angle. (Trove by Iteductio ad Absnrdum.) 2. If two lines are cut by a third, and the sum of the interior angles on the same side of the transversal is less than two right angles, the lines will meet if sufficiently produced. (I'rove by Reductio ad Absurdum.)...

...distant from the sides of the angle. (Prove by Beductio ad Absurdum.) 2. If two lines are cut by a third, and the sum of the interior angles on the same side of the transversal is less than two right angles, the lines will meet if sufficiently produced. (Prove by Beductio ad Absurdum.)...