Plane and solid geometry . Given AB II CD and AB ± plane prove CD _L plane MN. Argument 1. Through D draw any line in plane MN, as DF, 2. Through B draw BE in plane MN 1! DF. 3. Then Z ABE = Z CZ)i^. 4. But Z ^^^ is a rt. Z CDF is a rt. Z; Ci) ± Di^, any line in plane MN through D,.\ CD ± plane MN. 5. 6. Reasons 1. § 54, 15. 2. § 179. 3. § 635. 4. § 619. 5. § 54, 1. 6. § 619. Ex. 1168. In the accompanying diagram AB and CD lie in the sameplane. Angle CBA^So^, angle BCD = S6°,angle ABE = 90°, ^£ lying in plane MN. IsCD necessarily perpendicular to plane MN?Prove your ans
Plane and solid geometry . Given AB II CD and AB ± plane prove CD _L plane MN. Argument 1. Through D draw any line in plane MN, as DF, 2. Through B draw BE in plane MN 1! DF. 3. Then Z ABE = Z CZ)i^. 4. But Z ^^^ is a rt. Z CDF is a rt. Z; Ci) ± Di^, any line in plane MN through D,.\ CD ± plane MN. 5. 6. Reasons 1. § 54, 15. 2. § 179. 3. § 635. 4. § 619. 5. § 54, 1. 6. § 619. Ex. 1168. In the accompanying diagram AB and CD lie in the sameplane. Angle CBA^So^, angle BCD = S6°,angle ABE = 90°, ^£ lying in plane MN. IsCD necessarily perpendicular to plane MN?Prove your answer. Ex. 1169. Can a line be perpendicular toeach of two intersecting planes ? Prove. Ex. 1170. If one of two planes is per-pendicular to a given line, but the otheris not, the planes are not parallel. Ex. 1171. If a straight line and a plane are each perpendicular to thesame straight line, they are parallel to each 312 SOLID GEOMETRY Proposition XL Problem 637, Through a given point to construct a line per-pendicular to a given plane*
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
