Educ T 14 8.72, 280

RELATIONS OF LINES AND PLANES.

1. Through any point in space may be drawn,-
how many lines parallel to a given line?
how many planes parallel to a given line?
how many lines parallel to a given plane?
how many planes parallel to a given plane?
how many lines perpendicular to a given line?
how many planes perpendicular to a given line?
how many lines perpendicular to a given plane?
how many planes perpendicular to a given plane?
State and prove the relation which exists between-

si

two lines parallel to the same line;
two planes parallel to the same line;
two lines parallel to the same plane;
two planes parallel to the same plane;
two lines perpendicular to the same line;
two planes perpendicular to the same line;
two lines perpendicular to the same plane;

two planes perpendicular to the same plane.

3. Prove the following propositions:

I.

If a line is parallel to another line it is parallel to every` plane which contains that other line.

II. If a plane is parallel to a line it is not parallel to every plane which contains that line.

III.

If a plane is parallel to another plane it is parallel to every line contained in that other plane.

IV. If a line is parallel to a plane it is not parallel to every line contained in that plane.

V. If a line is perpendicular to another line it is not perpendicular to every plane which contains that other line. VI. If a plane is perpendicular to a line it is perpendicular to every plane which contains that line.

VII. If a plane is perpendicular to another plane it is not perpendicular to every line contained in that other plane.

VIII. If a lin

every

ane it is perpendicular to plane.

Fr. Остов