In the adjoining figure angleA=80°, BD fa Dase bisectors
of angleB angleB and angleC respectively. Then find angleBDC
Answers
Answer:
therefore (by I 5) each has in it the straight which
(by I i) is determined by these two points.
9. Corollary to 8. A point common to two planes
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RATIONAL GEOMETR Y.
lies in a straight common to the two, which may be
called their straight of intersection or their meet.
io. Theorem. A plane and a straight not lying in
it have no point or one point in common.
Proof. If they had two points in common the
straight would be (by I 5) situated completely in
the plane.
II. Theorem. Through a straight and a point not
on it there is always one and only one plane.
Proof. On the straight there are (by I 2) two
points. These two with the point not on the
straight determine (by I 3) a plane, in which (by
I 5) they and the given straight lie. Any plane
on this point and straight would be on the three
points already used, hence (by I 4) identical with
the plane determined.
12. Theorem. Through two different straights with
a common point there is always one and only one
plane.
Proof. Each straight has on it (by I 2) one
point besides the common point, and (by 6) these
two points are not the same point, and (by I 2)
the three points are not costraight.
These three points determine (by I 3) a plane in
which (by I 5) each of thetwo straights lies. Any
plane on these straights would be on the three
points already used, hence (by I 4) identical with
the plane determined.