Based on the figure, the statements that are true are
SV is perpendicular to TPSV is perpendicular to plane Apoint P lies on SV and in plane A
That is, the first, second and fifth statements.
From the image, we will determine the statements that are true based on the figure.
For the first statement - Ā SV is perpendicular to TP
From the figure,
SV is a line intersecting plane A at point P, at right angle. That is, SV is perpendicular to point P. Then, SV is perpendicular to plane A since point P lies on the plane.
Also, P lies on the plane (plane A); then we can infer that TP is parallel to plane A since point T also lie on the plane (plane A).
Since, SV is perpendicular to the plane, then SV is also perpendicular to TP.
ā“ The statement (SV is perpendicular to TP) is true
For the second statement - SV is perpendicular to plane A
As stated above, SV is perpendicular to point P. Since point P lies on the plane (plane A), then SV is perpendicular to plane A.
ā“ The statement (SV is perpendicular to plane A) is true
For the third statement - points S, P and Q are collinear
Collinear points are points that lie on the same line.
Points S, P and Q are not collinear because, a single line cannot pass through the three points, that is, the points (S, P, and Q) do not lie on a single line.
ā“ The statement (points S, P and Q are collinear) is NOT true
(From the image, an example of points that are collinear are points S, P, and V)
For the fourth statement - points R, T, and U are collinear
As explained above, points R, T, and U are not collinear because, a single line cannot pass through the three points, that is, the points (R, T, and U) do not lie on a single line.
ā“ The statement (points R, T and U are collinear) is NOT true
NOTE: (The points only lie in the same plane (plane A), that is, they are coplanar)
For the fifth statement - point P lies on SV and in plane A
Since line SV intersects plane A at point P, that means point P lies in plane A. Also point P lies on line SV since it is on the line as shown in the image.
ā“ The statement (point P lies on SV and in plane A) is true
For the sixth statement - points U, S, V, and Q are coplanar
Points or lines are said to be coplanar if they lie in the same plane.
Of the given points, only point U lies in plane A. Points S, V, and Q do not lie in the same plane and as well do not lie in the same plane as point U.
ā“ The statement (points U, S, V, and Q are coplanar) is NOT true.
(From the image, an example of points that are coplanar are points U,P,R, and T because they lie on the same plane).
Hence, based on the figure, the statements that are true are the first, second and fifth statements. that is
SV is perpendicular to TPSV is perpendicular to plane Apoint P lies on SV and in plane A
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