The Shed Problems

The figure on the right is a 3-dimensional drawing of a shed with no doors or windows.  Its roof, sides and floor are parts of seven different planes, which are referred to in the questions below.  Planes ABC and FGH (containing the front and back walls) are parallel, as are planes FAE and HCD (containing the left and right walls).  No other planes determined by the roof, walls or floor of this shed are parallel.

 

1.    Consider the front wall.  It contains the 5 points A, B, C, D, E, and any three of these can be used to name the plane of this wall.  For example, this plane can be named "plane ABC," it can be named "plane ACE," and so on.  Give 4 other names of this plane.

 

2.    Now consider the left part of the roof.  This contains the points A, B, G, F.  Its plane can be named by any three of these points.  For example, it can be named as "plane ABC," "plane AFG," and so on.  Give 2 other names of this plane.

 

3.    The plane determined by the roof (plane AFG) and the plane determined by the floor (plane QED) eventually intersect, as the following picture shows:

 

What geometric object is the intersection of these two planes?

4.    In general, if two different planes intersect, what geometric object is their intersection?  (This is stated in one of the postulates.)

5.    Consider the right wall which contains the points C, D, P, H.  Its plane, plane DPH, intersects the line as shown: 

Name the intersection of plane DCH and line AC. 

6.    In general, what geometric object is the intersection of a plane and a line not entirely contained in the plane?

7.    Now consider the plane determined by points E, C and H.  Points E and C are on a diagonal across the front wall, so this plane slants and does not contain any of the walls, roof or floor of the shed. Name a fourth point that is coplanar with points E, C and H.

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Answers

(1)  plane ACD, plane ADE, plane BCE, plane CDE (more answers possible)

(2)    plane ABG, plane BGF  (more answers possible)

(3)    a line (drawn in red)

(4)    a line

(5)    point C

(6)    a point

(7)    point Q

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