Use the above figure to answer the following questions. show your work if possible a. what is the intersection of plane p and plane r? b. name three points that are collinear c. name r in two more ways d. name four coplanar points

Part A

segment AB



another possible answer is segment AD. Segment BA is the same as segment AB. Segment DA is the same as segment AD. The order of the letters does not matter for segments.

All of the segments mentioned fall on the same line where the two planes intersect. This can be thought of as the book's spine in a sense (imagine the book is wide open, the pages are the planes)

Plane P is the horizontal plane
Plane R is the vertical plane



Part B

Point A, Point D, Point B



These three points all fall on the same line which means they are considered collinear. In other words, we can extend segment AD to have that line go through point B. Or put another way, segment AB has point D on it.



Part C

Plane DFG, plane GFA



To name a plane, we need to have three noncollinear points mentioned. These three noncollinear points must be in the plane we are naming. Think of it as naming a triangle that is entirely in the plane. Two points aren't enough because we can have two planes through a single segment (as part A shows). Points D, F, A, G, B all are in plane R. So you just pick three of those points to name the plane. 

Note: you cannot pick A, B, and D together because you must pick three noncollinear points. Otherwise you run into the problem mentioned earlier (having 2 planes go through the same segment)



Part D

Point A, Point B, Point D, Point F



All of the points mentioned are in the same plane. They are all in plane R (the vertical plane). Point G is also in plane R, but I left it out because your teacher only wants 4 coplanar points.

Another possible answer is listing any four points in plane P, such as this set {point C, point D, point E, point A} which all are located in the horizontal plane.