Question

1. which statement is true?

a. points v, x, and w are coplanar
b. plane svt and plane vuy intersect at point x
c. segments sv and xy are coplanar
d. points s, t, and u are coplanar

1. what is the intersection of plane yzvu and plane zwsv?

a. line segment vz
b. point v
c. line vu
d. point x

Explanation:

Question 7

Option A

Points \(V\), \(X\), and \(W\) are not coplanar. Point \(V\) is on the top - front - left face, \(W\) is on the bottom - front - left face, and \(X\) is on the bottom - back - right face.

Option B

Planes \(SVT\) and \(V UY\) do not intersect at point \(X\). Planes intersect along a line, not a single point (unless the planes are the same, which they are not here).

Option C

Segments \(SV\) and \(XY\) are not coplanar. \(SV\) is on the left - front face, and \(XY\) is on the bottom - back face.

Option D

Points \(S\), \(T\), and \(U\) are on the top face of the rectangular prism. By the definition of a plane (a flat, two - dimensional surface), three non - collinear points on a flat surface are coplanar.

Question 8

Option A

Plane \(YZVU\) and plane \(ZWSV\) share the line segment \(VZ\). A line is the intersection of two non - parallel planes.

Option B

A single point (\(V\)) cannot be the intersection of two planes (since planes are two - dimensional and their intersection is at least a line).

Option C

Line \(VU\) is not common to both planes \(YZVU\) and \(ZWSV\).

Option D

Point \(X\) is not on either plane \(YZVU\) or \(ZWSV\).

Answer:

1. D. points \(S\), \(T\), and \(U\) are coplanar
2. A. line segment \(VZ\)