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Solid Geometry Notes
0
How is a plane defined? What is meant by foot of a straight line on
a plane?
1
What is meant by two or more geometrical objects determining a
plane?
2
Two intersecting straight lines determine a plane. Therfore, straight
line and a point not on it, three non collinear points, two parallel
lines determine a plane.
3
If two planes intersect, they do so in a straight line.
4
What is meant by a straight line perpendicular to a plane and vice
versa?
5
If a line is perpenducular to each of intersecting lines at their point
of intersection, the line is perpendicular to the plane of the
intersecting lines.
6
All the perpendiculars that can be drawn to a given line at a given
point lie in a plane which is perpendicular to the given line at the
given point. Therfore, through a given point on a given plane one
and only one plane exists that is perpendicular to given line. Also,
through a point not on a given line one and only one plane exists
that is perpendicular to given line.
7
What is meant by oblique line?
8
Through a given point on a given plane, one and only one line
exists that is perpendicular to given plane and passing through
given point.
9
Through a given point not on a given plane, one and only one line
exists that is perpendicular to given plane and passing through
given point.
10
What is meant by distance of a point from the plane?
11
Oblique lines which meet the plane at equal distance from the foot
of the perpendicular are equal. The oblique line which meet the
plane at a greater distance from the foot of perpendicular is greater.
And the converse holds.
12
Two lines perpendicular to the same plane are parallel.
13
If one of two parallel lines is perpendicular to a plane, the other is
also perpendicular to the plane.
14
Two lines parallel to the third are parallel to each other.
15
What is meant by a line and a plane parallel?
16
A plane passing through one and only one of two parallel lines is
parallel to the other line.
17
Through either of two lines not in same plane, one and only plane
exists parallel to the other.
18
Through a given point , one and only one plane exists which is
parallel to two given lines.
19
What are called parallel planes?
EXERCISE
20
Two planes perpendicular to same line are parallel.
21
The intersection of parallel planes with any plane is parallel lines.
22
Parallel lines between parallel planes are equal.
23
What is meant by distance between parallel planes?
24
A line perpendicular to one of the parallel planes is perpendicular
to the other.
25
Through a given point not on a given plane, one and only one
plane exists parallel to given plane.
26
If two intersecting lines are each parallel to a plane, their plane is
parallel to this plane.
27
If two angles, not on the same plane have their sides parallel and
lie on the same side then their planes are parallel and angles are
equal.
28
If two lines are cut by three parallel planes, their corresponding
segments are proportional.
EXERCISE
29
What is meant by dihedral angle, adjacent dihedral angles, right
dihedral angle?
30
What are perpendicular planes?
31
What is meant by plane angle of the dihedral angle?
32
Two dihedral angles are equal if their plane angles are equal.
33
If two planes are perpendicular then a line drawn in one of them
perpendicular to their intersection is perpendicular to the other
plane. And the converse holds.
34
If a line is perpendicular to a plane then every plane passing
through this line is perpendicular to the plane.
35
If two intersecting planes are each perpendicular to a third plane
then their intersection is also perpendicular to that plane.
36
Through a given line not on a given plane and not perpendicular to
it, one and only one plane exists perpendicular to the given plane.
37
What is meant by projection of a point and projection of a line on a
plane? How can the projection of a line on a plane be fixed?What
is meant by inclination of a line to a plane?
38
The angle made by a line with it’s projection on a plane is the least
of angles made by line with any other line on the plane.
39
Between two lines not in the same plane there exists one and only
one common perpendicular.
40
What is meant by polyhedral angle?
Prepared from D E Smith Solid Geometry