Points, lines and planes are undefined terms in geometry.
The true statements are:
- (c) V lies on line ST
- (d) ST is perpendicular to plane A
- (e) ST is perpendicular to RV
First, we test each option to determine the true and false options.
(a) S, V and U are collinear
Points that are collinear are on the same line
S, V and U are not collinear, because they are not on the same line.
Hence, (a) is false
(b) Q, S, T and U are coplanar
Points that are coplanar are on the same plane
Q, S, T and U are not coplanar, because they are not on the same plane.
Hence, (b) is false
(c) V lies on line ST
Point V is the point of intersection of line ST and plane A
This means that point V lies on line ST and plane A
Hence, (c) is true
(d) ST is perpendicular to plane A
Line ST intersects with plane A at point V at 90 degrees.
Perpendicular lines and planes meet at 90 degrees
Hence, (d) is true
(e) ST is perpendicular to RV
Because line ST intersects with plane A at point V at 90 degrees.
Any line drawn from point V would be perpendicular to line ST
Hence, (e) is true
(f) P, R and Q are collinear
Points that are collinear are on the same line
P, R and Q are not collinear, because they are not on the same line.
Hence, (f) is false
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