Question

In the figure of a cube,

i) Which edge is the intersection of faces EFGH and EFBA?
ii) Which faces intersect at edge FB?
iii) Which three faces form the vertex A?
iv) Which vertex is formed by the faces ABCD, ADHE and CDHG?
v) Give all the edges that are parallel to edge AB
vi) Give the edges that are neither parallel nor perpendicular to edge BC.
vii) Give all the edges that are perpendicular to edge AB.
viii) Give four vertices that do not all lie in one plane.

[4 marks]

Answer 1

i) From the given figure, we can observe that EF is the intersection of faces EFGH and EFBA.
[0.5 mark]

ii) From the given figure, we can observe that faces EFBA and FBCG intersect at edge FB.
[0.5 mark]

iii) Faces ABFE, ADHE and ABCD form the vertex A.
[0.5 mark]

iv) Vertex D is formed by the faces ABCD, CDHG and ADHE.
[0.5 mark]

v) The edges parallel to edge AB are CD, EF and HG.
[0.5 mark]

vi) From the given figure, we can observe that edges AE, EF, GH and HD are neither parallel nor perpendicular to edge BC.
[0.5 mark]

vii) From the given figure, we can observe that edges AE, BF, AD and BC are perpendicular to edge AB.
[0.5 mark]

viii) Vertices A, B, G and H do not lie in one plane.
[0.5 mark]