Solid Geometry

Cover Solid Geometry
Solid Geometry
C Charles Godfrey
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4) are cut by the parallel planes a, /3, y (note that AEB, CFD are not necessarily in the same plane).
10 SOLID GEOMETRY To prove that AE : EB = CF : FD.
Proof Let AD meet the plane /? in X.
Join AC, BD, EX, XF.
The plane ABD cuts || planes ^, y in || lines EX, BD.
. '. AE: EB = AX : XD.
Similarly, CF : FD == AX : XD.
. '. AE: EB = CF : FD.
A E W . .
fi 1 L .
Li. - Ex. 35. In what case are E, X, F in a straight line? (fig. 4. ) Ex. 36. In what ease are AC and BD parallel? (fig. 4. ) fEx. 37. Po
...ints A, B, C, D in a plane are joined to a point O not in the plane. OA, OB, OC, CD are divided in the same ratio at A', B', C, D'. Prove that A'B'C'D' is a plane quadrilateral similar to ABCD. (Let plane A'B'C cut CD in X ; shew that X coincides with D'. ) Ex. 38. A stick 1 foot long is placed inside a box 10 inches high, touching the top and bottom. Prove that the locus of any point on the stick is a plane.
CHAPTER III.
PERPENDICULAR POSITIONS OF LINES AND PLANES.
It is obvious that if a line is perpendicular to a plane, it is perpendicular to any line that lies in that plane and meets it.


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