In the figure 12.24 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.
Solution:
(i) In the figure,
We see that EF is the intersection of faces EFGH and EFBA.
(ii) In the figure,
We see that faces EFBA and FBCG intersect at the edge FB.
(iii) The three faces which form the vertex A are ABFE, ADHE and ABCD.
(iv) Vertex D is formed by the faces ABCD, ADHE and CDHG.
(v) All the edges that are parallel to edge AB are CD, EF and HG.
(vi) In the figure,
We see that the edges AE, BF, GH and HD are neither parallel nor perpendicular to edge BC.
(vii) In the figure,
We see that the edges AE, BF, AD and BC are perpendicular to edge AB.
(viii) The vertices A, B, G and H do not lie in one plane.
✦ Try This: Construct an equilateral triangle XYZ of side 12 cm.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 10
NCERT Exemplar Class 7 Maths Chapter 12 Problem 104
In the figure 12.24 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
Summary:
In the figure 12.24 of a cube, (i) EF is the intersection of faces EFGH and EFBA, (ii) The faces EFBA and FBCG intersect at the edge FB, (iii) The three faces which form the vertex A are ABFE, ADHE and ABCD, (iv) Vertex D is formed by the faces ABCD, ADHE and CDHG, (v) All the edges that are parallel to edge AB are CD, EF and HG, (vi) The edges AE, BF, GH and HD are neither parallel nor perpendicular to edge BC, (vii) The edges AE, BF, AD and BC are perpendicular to edge AB, (viii) The vertices A, B, G and H do not lie in one plane.
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