1.
Another name for a corner, or point, is
Correct Answer
C. Vertex
Explanation
A vertex is a point where two or more lines or edges meet. It is also referred to as a corner. In geometry, a vertex is an important element in defining the shape and structure of a polygon. It is the point where the sides of the polygon intersect, forming angles. Therefore, vertex is the correct answer for another name for a corner or point.
2.
On a cube, there are a total of
Correct Answer
C. 6 faces and 12 edges
Explanation
A cube has 6 faces, each of which is a square. Each face of the cube is connected to 4 other faces, resulting in a total of 12 edges. Therefore, the correct answer is 6 faces and 12 edges.
3.
Every polygon must have the same number of
Correct Answer
A. Edges as vertices
Explanation
In a polygon, each vertex is connected to two edges, and each edge is connected to two vertices. Therefore, the number of edges is always equal to the number of vertices. Hence, the correct answer is "edges as vertices".
4.
If you truncate one vertex of the dodecahedron shown, the new face created will be a
Correct Answer
A. Triangle
Explanation
When a vertex of a dodecahedron is truncated, it creates a new face with three sides, which is a triangle. Truncating a vertex involves cutting off a portion of the dodecahedron, resulting in a flat surface that connects three adjacent vertices. This new face will have three straight sides, forming a triangle shape. Therefore, the correct answer is triangle.
5.
How many Platonic Solids are there?
Correct Answer
B. Five
Explanation
There are five Platonic Solids. These are regular polyhedra, meaning that all of their faces are congruent regular polygons, and their vertices are equidistant from the center. The five Platonic Solids are the tetrahedron (4 faces), cube (6 faces), octahedron (8 faces), dodecahedron (12 faces), and icosahedron (20 faces).
6.
Which of the following is NOT a Platonic Solid?
Correct Answer
C. Rhombohedron
Explanation
A rhombohedron is not a Platonic solid because it does not meet the criteria of having congruent faces, edges, and vertices. A rhombohedron is a parallelepiped with six congruent rhombus faces, but its edges and vertices are not all congruent. In contrast, a Platonic solid, such as a tetrahedron, octahedron, or icosahedron, has congruent faces, edges, and vertices, making it a regular polyhedron.
7.
In the topic of polyhedrons and polygons, "regular" means
Correct Answer
C. All edges are equal length
Explanation
In the topic of polyhedrons and polygons, the term "regular" refers to shapes where all edges are of equal length. This means that every side of the shape has the same measurement, resulting in a symmetrical and balanced structure. The other options mentioned, such as being shaped correctly or having a specific number of faces, do not accurately define what it means for a shape to be "regular" in this context.
8.
The shape in the diagram below is not a regular polyhedron because it has
Correct Answer
B. Faces that are different shapes
Explanation
The shape in the diagram is not a regular polyhedron because it has faces that are different shapes. A regular polyhedron is a three-dimensional solid with faces that are all congruent regular polygons. In this case, the shape has faces that are not all the same shape, which means it does not meet the criteria to be classified as a regular polyhedron.
9.
An architect want to make a skylight which has the shape of an icosahedron. She will need panes of glass which are
Correct Answer
A. Triangular
Explanation
The architect will need triangular panes of glass to create a skylight in the shape of an icosahedron. Since an icosahedron is a polyhedron with 20 triangular faces, it makes sense that triangular panes would be required. The other options, such as various sizes, square, or hexagonal, do not align with the shape of an icosahedron.
10.
Which of the following shapes can NOT be fit together to make a regular polyhedron?
Correct Answer
A. Octagon
Explanation
An octagon cannot be fit together with other shapes to make a regular polyhedron because a regular polyhedron is made up of identical regular polygons, and an octagon is not a regular polygon. A regular polygon has all sides and angles equal, while an octagon has sides and angles of different lengths and measures. Therefore, it is not possible to create a regular polyhedron using octagons.
11.
The prefix "poly" means
Correct Answer
C. Many
Explanation
The prefix "poly" is derived from the Greek word "polys" which means "many." It is commonly used in English to indicate a large quantity or a variety of something. For example, words like "polygamy" (having multiple spouses) or "polysyllabic" (having many syllables) use this prefix to convey the meaning of "many." Therefore, the correct answer is "many."
12.
What is another name for a cube?
Correct Answer
B. Hexahedron
Explanation
A hexahedron is another name for a cube. A cube is a three-dimensional shape with six equal square faces. A hexahedron is a polyhedron with six faces, and in the case of a cube, all the faces are squares. Therefore, hexahedron is the correct answer as it accurately describes the shape of a cube.