Geometry, Angles, Chapter Review

Front

What is Euler's formula for polyhedra?

Back

Euler's formula states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) are related by the equation: V - E + F = 2.

Front

How do you calculate the number of faces on a polyhedron using Euler's formula?

Back

Rearranging Euler's formula, F = E - V + 2. For a polyhedron with 10 edges and 6 vertices, F = 10 - 6 + 2 = 6.

Front

What is a vertex in geometry?

Back

A vertex is a point where two or more lines or edges meet. In polyhedra, vertices are the corners of the shape.

Front

Define an edge in the context of polyhedra.

Back

An edge is a line segment that connects two vertices in a polyhedron.

Front

What is a face in geometry?

Back

A face is a flat surface that forms part of the boundary of a solid object. In polyhedra, faces are typically polygons.

Front

What is the relationship between edges, vertices, and faces in a polyhedron?

Back

According to Euler's formula, the relationship is V - E + F = 2.

Front

If a polyhedron has 8 vertices and 12 edges, how many faces does it have?

Back

Using Euler's formula: F = E - V + 2 = 12 - 8 + 2 = 6.

Front

What is the value of 'b' if it is defined as 120?

Back

The value of 'b' is 120.

Front

What is the value of 'a' if it is defined as 105?

Back

The value of 'a' is 105.

Front

What is the value of 'b' if it is defined as 77?

Back

The value of 'b' is 77.