Question

how could you characterize the relationship between faces abcd and dcgh? explain.
abcd and dcgh could be characterized as
select choice
, because
select choice
contains segment cg, which is
select choice
to
select choice

Explanation:

Step1: Identify the shape

The figure is a rectangular prism (a box - shaped figure with six rectangular faces).

Step2: Analyze the faces ABCD and DCGH

In a rectangular prism, adjacent faces meet at a right angle (are perpendicular) if they share an edge and the edge is perpendicular to the plane of the other face. Face ABCD and face DCGH share the edge DC. Let's consider the edges: In face ABCD, the edges are AB, BC, CD, DA. In face DCGH, the edges are DC, CG, GH, HD. The edge DC is common. Now, look at the angle between the two faces. The face ABCD is a rectangle, and face DCGH is also a rectangle. The edge CG is part of face DCGH, and DC is part of both faces. The angle between DC and CG is 90 degrees (since it's a rectangular prism, the edges meeting at a vertex are perpendicular). So, the two faces ABCD and DCGH are perpendicular because they share a common edge (DC) and the adjacent edges (like CG and BC) are perpendicular. Also, face DCGH contains segment CG, which is perpendicular to segment DC (since in the rectangular prism, the edges are perpendicular to each other at the vertices).

Answer:

The relationship between faces ABCD and DCGH is that they are perpendicular. Face DCGH contains segment CG, which is perpendicular to segment DC (a side of face ABCD). So, the first "Select Choice" should be "perpendicular", the second "Select Choice" (the face) is "DCGH", the third "Select Choice" (the relationship of CG to DC) is "perpendicular", and the fourth "Select Choice" (the side of ABCD) is "DC".