Question

1) ABCDA1B1C1D1 - параллелепипед. Е принадлежит DD1; М принадлежит AB; K принадлежит BC. Построить сечение (MEK). 2) ABCDA1B1C1D1 - параллелепипед. М принадлежит BB1. Построить сечение (ADM). 3. DABC - тетраэдр. М принадлежит BC; N принадлежит DC; K принадлежит AD. Построить сечение (MNK). 4) MABC - тетраэдр. E принадлежит MB; K принадлежит AB; N принадлежит AC. Построить сечение (EKN).

Answer 1

1) MK лежит в плоскости ACD. Находим пересечения с AD (X) и CD (Y).

XE лежит в плоскости ADD1. Находим пересечение с AA1 (F).

YE лежит в плоскости CDD1. Находим пересечение с CC1 (G).  

2) Секущая плоскость проходит через параллельные грани. MK||AD.

Answer 2

To construct the specified sections, we need to draw the intersection lines on each solid. Here are the steps for each case:

1. ABCDA1B1C1D1 - Parallelepiped. E belongs to DD1; M belongs to AB; K belongs to BC. Construct the section (MEK).

Step 1: Draw the parallelepiped ABCDA1B1C1D1.

Step 2: Draw the line ME parallel to AB and passing through D1.

Step 3: Draw the line EK parallel to BC and passing through A1.

Step 4: The section (MEK) is the triangle formed by the points M, E, and K.

2. ABCDA1B1C1D1 - Parallelepiped. M belongs to BB1. Construct the section (ADM).

Step 1: Draw the parallelepiped ABCDA1B1C1D1.

Step 2: Draw the line AD parallel to BB1 and passing through C1.

Step 3: The section (ADM) is the triangle formed by the points A, D, and M.

3. DABC - Tetrahedron. M belongs to BC; N belongs to DC; K belongs to AD. Construct the section (MNK).

Step 1: Draw the tetrahedron DABC.

Step 2: Draw the line MN parallel to AD and passing through B.

Step 3: Draw the line NK parallel to DC and passing through A.

Step 4: Draw the line MK parallel to BC and passing through D.

Step 5: The section (MNK) is the triangle formed by the points M, N, and K.

4. MABC - Tetrahedron. E belongs to MB; K belongs to AB; N belongs to AC. Construct the section (EKN).

Step 1: Draw the tetrahedron MABC.

Step 2: Draw the line EK parallel to AC and passing through B.

Step 3: Draw the line EN parallel to AB and passing through C.

Step 4: The section (EKN) is the triangle formed by the points E, K, and N.

Remember that constructing sections involves drawing lines parallel to certain edges of the solid and passing through specific points. These lines represent the intersections of the solid with the plane containing the given points.