MONGE PROJECTION. PERPENDICULARITY

1.

Construct projections of rectangular prism (right prism) AA

1

BB

1

CC

1

DD

1

. The base of

prism is a square ABCD which belongs to plane



. Plane of square is perpendicular

to vertical projection plane. Projections of one side of square, section AB are given.
The length of

side’s edges of prism is 7 cm.

2.

Construct projections of right prism AA

1

BB

1

CC

1

. The base of prism is equilateral

triangle ABC which belongs to plane



. Plane of triangle is perpendicular to horizontal

projection plane. Projections of one side of triangle, section AB are given. The length
of side

’s edges of prism is 8 cm.

3.

Construct projections of right pyramid ABCDW. The base of pyramid is a square
ABCD which belongs to plane



. Plane of square is perpendicular to horizontal

projection plane. Projections of one side of square, section AB are given. The length
of height of pyramid is 8 cm.

4.

Construct projections of regular tetrahedron ABCD (all walls are equilateral triangles).
The base of tetrahedron, triangle ABC belongs to plane



. Plane



is perpendicular to

vertical projection plane. The angle between plane



and horizontal projection plane is

30

o

. Horizontal projection of one side of triangle ABC, section AB is given and vertical

projection of point A (vertex of triangle ABC) is given too.

5.

Projections of triangle ABC are given, plane of triangle is perpendicular to horizontal
projection plane. Construct projections of right pyramid ABCW. Triangle ABC is a
base of pyramid, the height of pyramid segment SW is perpendicular to the base
(right pyramid ). The length of segment SW is 7 cm. Point S is a centre of circle
described on triangle ABC.

6.

Construct projections of cube AA

1

BB

1

CC

1

DD

1

. Base of cube, square ABCD belongs

to plane



. Plane



is perpendicular to horizontal projection plane, an angle between



and vertical projection plane is 45

o

. Vertical projection of one side of square,

segment AB is given, horizontal projection of point A, vertex of cube is given too.

7.

Construct projection of right prism AA

1

BB

1

CC

1

. The base of prism is right, isosceles

triangle ABC (the length of segments AB and AC are the same). Triangle ABC
belongs to plane



. Plane



is perpendicular to horizontal projection plane. Length of

prism

’s side’s edge is 7 cm. Projection of one side of triangle ABC, segment AB are

given.