...diedral angles are equal ; the corresponding diedral angles are equal. PROPOSITION XVIII. THEOREM 564 If two planes are perpendicular to each other, a straight...their intersection is perpendicular to the other. p/A HYPOTHESIS. SQ is the intersection of the perpendicular planes MN and PQ, and AB in PQ is -L to...

...are equal ; the corresponding diedral angles are equal. DIEDRAL ANGLES PROPOSITION XVIII. THEOREM 564 If two planes are perpendicular to each other, a straight...their intersection is perpendicular to the other. HYPOTHESIS. SQ is the intersection of the perpendicular planes MN and PQ, and AB in PQ is JL to SQ...

...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....

.../ / 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...

...** 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...

...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...