...plane, a plane can be drawn perpendicular to the given plane, and but one. PROP. XXIII. THEOREM 387. If two planes are perpendicular to each other, a straight...their intersection is 'perpendicular to the other. Given planes PQ and MN -L, intersecting in line QB, and linn AB in plane PQ JL QR. To Prove AB J- MN....

...Computation. 1. From D draw DO _L J&F7, and in the plane EC draw GH ± EF, cutting .BG' at If.' Then GH1. QR. (If two planes are perpendicular to each other, a...their intersection is perpendicular to the other.) § 387. 2. Then plane DGHA _L EF. (All the perpendiculars to a straight line at a given point lie in...

...teachers omit the proposition that two dihedral angles have the same ratio as their plane angles. THEOREM. If two planes are perpendicular to each other, a straight...their intersection is perpendicular to the other. This and the related propositions allow of numerous illustrations taken from the schoolroom, as of...

...right Z , (for AB _L JfJV6^ hyp.). :. PQ ± Art. 505. Art. 547. QED PROPOSITION XVIII. THEOREM 557. If two planes are perpendicular to each other, a straight line drawn in one of them perpendicular to their t line of intersection is perpendicular to the other plane. Given the plane PQ _L plane MN and intersecting...

...straight lines are cut by three parallel planes, the lines are divided proportionally. 11. Prove that if two planes are perpendicular to each other, a straight line drawn in one plane, perpendicular to the intersection of the two planes, is perpendicular to the other plane. 12....

...** AT B n / PROPOSITION XXIII. THEOREM 679. If two planes are perpendicular to each other, any line in one of them, perpendicular to their intersection, is perpendicular to the other. N Given plane PQ _L plane MN, CD their line of intersection, and AH, in plane PQ, JL CD. To prove AB...

.../ / BOOK VI PROPOSITION XXIII. THEOREM 679. If two planes are perpendicular to each other, any line in one of them, perpendicular to their intersection, is perpendicular to the other. E: Given plane PQ _L plane MN, CD their line of intersection, and Ali, in plane PQ, _L CD. To prove...

...straight line to construct a plane perpendicular to a given plane. PROPOSITION XVIII. THEOREM 529. If two planes are perpendicular to each other, a straight...their intersection, is perpendicular to the other. Given plane CE _L plane MN, and in CE line BA _L CD, the intersection of the two planes. To prove AB...

...=^ABD'^*™- . «•*•*• PROPOSITION XVII. THEOREM 474. If two planes are perpendicular to each other, a line drawn in one of them perpendicular to their intersection is perpendicular to the other. Given the planes MN and PQ perpendicular to each other, and the line CD in PQ perpendicular to their...

...the dihedral angle. PROPOSITION XVII. THEOREM 474. If tioo planes are perpendicular to each other, a line drawn in one of them perpendicular to their intersection is perpendicular to the other. §473 Given QED Given the planes MN and PQ perpendicular to each other, and the line CD in PQ perpendicular...