Plane and solid geometry . Given plane PQ ± plane MN^ CD their line of intersection,and AB, in plane PQ, 1. prove AB Jl plane MN. Argument 1. Through B, in plane MN, draw BE J. CD. 2. Then Z ABE is the plane Z of the rt. dihedral Z Q-CD-M. 3. .-. Z ABE is a rt. Z, and AB ± BE. 4. But AB ± CD. 6. .% ^5 JL plane MN. Reasons 1. §63. 2. §670. 3. §674. 4. By §622. 680. Cor. If two planes are perpendicular to eachother, a line perpendicular to one of them at any pointin their line of intersection, lies in the other. Hint. Apply the indirect method, using §§ 679 and 638. Ex. 1213.

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Plane and solid geometry . Given plane PQ ± plane MN^ CD their line of intersection,and AB, in plane PQ, 1. prove AB Jl plane MN. Argument 1. Through B, in plane MN, draw BE J. CD. 2. Then Z ABE is the plane Z of the rt. dihedral Z Q-CD-M. 3. .-. Z ABE is a rt. Z, and AB ± BE. 4. But AB ± CD. 6. .% ^5 JL plane MN. Reasons 1. §63. 2. §670. 3. §674. 4. By §622. 680. Cor. If two planes are perpendicular to eachother, a line perpendicular to one of them at any pointin their line of intersection, lies in the other. Hint. Apply the indirect method, using §§ 679 and 638. Ex. 1213. If a plane is perpendicular to the edge of a dihedral angle,is it perpendicular to each of the faces of the dihedral angle ? Prove youranswer. Ex. 1214. The plane containing a straight line and its projectionupon a plane is perpendicular to the given plane. Ex. 1215. If two planes are perpendicular to each other, a line per-pendicular to one of them from any point in the other lies in the otherplane. 330 SOLID GE

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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912