Positional properties

1103059503

Level: 
B
Let ABCDEFGH be a cube. What is the mutual position of planes ECG, BDF, and ABH?
three mutually intersecting planes which share one common point
three mutually intersecting planes which share one common line
two planes are parallel with the third intersecting them in distinct parallel lines

1103059504

Level: 
B
Let ABCDEFGH be a cube with K, and L being the midpoints of its edges AE and CG, and let M be the centre of its face ABFE. What is the mutual position of planes BCE, ADF, and KLM?
three mutually intersecting planes which share one common line
three mutually intersecting planes which share one common point
two planes are parallel with the third intersecting them in distinct parallel lines

1103059505

Level: 
B
Let ABCDEFGH be a cube and X be the midpoint of its edge AE. What is the cross-section of the cube if we slice it with a plane BGX?
a quadrilateral BGPX with P being the midpoint of the edge EH
a quadrilateral BGHX
a triangle BGX
a quadrilateral BGPX with P being the midpoint of the edge DH

1103059506

Level: 
B
Let ABCDEFGH be a cube and let X, Y, and Z be the midpoints of edges AB, AE, and CG respectively. What is the cross-section of the cube if we slice it with a plane XYZ?
a hexagon XLZKMY with points L, K, and M lying on edges BC, GH, and EH respectively
a pentagon XLZKY with points L and K lying on edges BC and GH respectively
a triangle XYZ
a quadrilateral XZKY with K being the midpoint of the edge GH

1103059507

Level: 
B
Let ABCDEFGH be a cube with K and L being the midpoints of edges AE and AB respectively, and let M be the midpoint of the face diagonal EG. What is the cross-section of the cube if we slice it with a plane KLM?
a pentagon KLPQR with points P, Q, and R lying on edges BC, FG, and EH respectively
a triangle KLM
a pentagon KLPQM with points P and Q lying on edges BC and FG respectively
a quadrilateral KLMR with point R lying on the edge EH

1103059601

Level: 
B
Let ABCDV be a rectangle based-pyramid and V its apex. The pyramid is sliced by a plane EFG which is defined by: E∈BC ∧ |BE|=2|CE|,F∈AV ∧ |AF|=2|VF|,G∈DV ∧ |DG|=2|VG| (see the picture). What is the cross-section of the pyramid if we slice it with the plane EFG?
a trapezium BCGF
a triangle EFG
a triangle AEV
a pentagon ABEGF

1103059602

Level: 
B
Let ABCDV be a rectangle based-pyramid and V its apex. The pyramid is sliced by a plane XYZ which is defined by: X is the midpoint of the edge AD,Y∈CD ∧ |DY|=3|CY|,Z∈BV ∧ |BZ|=3|VZ| (see the picture). What is the cross-section of the pyramid if we slice it with the plane XYZ?
a pentagon XYKZL with points K and L lying on the edges CV and AV
a triangle XYZ
a quadrilateral XYZL with point L lying on the edge AV
a quadrilateral XYKZ with point K lying on the edge CV

1103059603

Level: 
B
Let ABCDEFGH be a cube and let XY be a line where: X lays on a ray BC and |BX|=1.5|BC|,Y lays on a ray HE and |HY|=1.5|HE| (see the picture). The points of intersection of the line XY with the surface of the cube lay:
on the sides ABFE and DCGH
on the side ABFE and the edge CG
on the edges AE and CG
on the sides ADHE and BCGF