...has been proved equal to GHD; therefore, EGB is also equal to GHD. Add to each of these equals the angle BGH; then will the sum of EGB, BGH be equal...II.); therefore, also, BGH, GHD are equal to two right angles. Therefore, if a straight line, &c Cor. 1. If a straight line is perpendicular to one of two...

...AGH has been proved equal to GHD; therefore, EGB is also equa to GHD. Add to each of these equals the angle BGH; then will the sum of EGB, BGH be equal...right an gles. Therefore, if a straight line, &c Cor. 2. If two lines, KL and CD, make with EF the two angles KGH, GHC together less than two right angles,...

...has been proved equal to GHD ; therefore, EGB is also equa to GHD. Add to each of these equals the angle BGH; then will the sum of EGB, BGH be equal...Cor. 1. If a straight line is perpendicular to one of twc parallel lines, it is also perpendicular to the other. Cor. 2. If two lines, KL and CD, make with...

...assuming that any line other than AB can be drawn through F parallel to CD. Therefore, AB is parallel. Cor. 1. — If a straight line is perpendicular to one of two parallels, it is perpendicular to the other (?). BFG + FGD = 2 L's. But, by hypothesis, EF is perpendicular...

...they are parallel. This method of proof is called the indirect method. PROPOSITION VII. THEOREM. 102. If a straight line is perpendicular to one of two parallel lines, it is perpendicular to the other. H: o -It E K Let AB and EF be two parallel lines, and let HK 63 perpendicular...

...produced. 5. .'. AB and CZ>are parallel. By definition of Parallel Lines. PROPOSITION VII. I. Theorem. If a straight line is perpendicular to one of two parallel lines, it is perpendicular to the other, H CII. III. .K Given the parallel lines AB and CD and the line /fA' perpendicular...

...judge end not because the majortiy use the science. The course of reasoning by which we prove, "If one straight line Is perpendicular to one of two parallel lines, it is perpendicular to the other," is not gone through with to ascertain tbe truth of a statement so evident,...

...same plane perpendicular to a third line are parallel to each other. Proposition VII. A Theorem. 39. If a straight line is perpendicular to one of two parallel lines, it is perpendicular to the other also. Proposition VIII. A Theorem. 40. Angles having the sides of the one...

...same plane perpendicular to a third line are parallel to each other. Proposition VII. A Theorem. 39. If a straight line is perpendicular to one of two parallel lines, it is perpendicular to the other also. Proposition VIII. A Theorem. 40. Angles having the sides of the one...

...given point, one straight line, and only one, can be drawn parallel to a given straight line. 102. If a straight , line is perpendicular to one of two parallel lines, it is perpendicular to the other. 104. If two parallel straight lines are cut by a third straight line, the...