Final answer:
In a square-based pyramid, there are no vertices formed by 2 edges, 4 vertices are formed by 3 edges at the pyramid's base, and 1 vertex is formed by 4 edges at the apex.
Step-by-step explanation:
How many vertices on a square-based pyramid are formed by joining different numbers of edges?
- a) 2 edges: No vertices of a square-based pyramid are formed by only joining 2 edges. Each vertex is formed by the intersection of at least 3 edges.
- b) 3 edges: There are 4 vertices at the base of the pyramid, each formed by the intersection of 3 edges (2 from the base and 1 from the side).
- c) 4 edges: There is only 1 vertex at the tip of the pyramid where 4 edges meet (all 4 from the sides of the pyramid).
Therefore, in a square-based pyramid, 4 vertices are formed by 3 edges each at the base, and 1 vertex is formed by 4 edges at the apex.