a. The plane passes through the midpoint of XW as well. This means that XW is also a part of the plane P.
b. The plane passes through the midpoint of XV as well. This means that XV is also a part of the plane P.
c. The plane P contains the entire quadrilateral VXZVW.
Given that Plane P is a perpendicular bisector of XZ at point Y, we need to prove the following statements:
a. XW = ZW
b. XV = ZV
c. ∠VXW= ∠VZW
Proof of Statements:
a. XWZW
Given that Plane P is a perpendicular bisector of XZ at point Y, this means that the plane passes through the midpoint of XZ. Since XZ is a line segment, its midpoint is the average of the endpoints, which are X and Z. Therefore, the plane passes through the midpoint of XW as well. This means that XW is also a part of the plane P.
b. XV ZV
Since Plane P is a perpendicular bisector of XZ at point Y, it passes through the midpoint of XZ. The midpoint of XZ is the average of the endpoints, which are X and Z. Therefore, the plane passes through the midpoint of XV as well. This means that XV is also a part of the plane P.
c. ∠VXW= ∠VZW
Since Plane P is a perpendicular bisector of XZ at point Y, it passes through the midpoint of XZ. The midpoint of XZ is the average of the endpoints, which are X and Z. Therefore, the plane passes through the midpoint of VX as well. This means that VX is also a part of the plane P. Since the plane passes through points X, V, and X, it also passes through all points on the line segment XVX.
Therefore, the plane P contains the entire line segment VX. Since the plane P also passes through point Z, it contains the entire line segment VZ as well. Therefore, the plane P contains the entire quadrilateral VXZVW.