Math Plus Warm Up: Triangles In A Pentagon

Give one or two warm up problems at beginning of every math class. Encourage students' discussions and be open minded to different possible answers.



















Answer:
There are 35 triangles (5 triangles have two sides that are sides of the pentagon, 20 triangles have exactly one side that is side of the pentagon, 10 triangles have sides that are not sides of the pentagon - 5 of them have exactly two vertices that are vertices of the pentagon, and 5 of them have exactly one vertex that is a vertex of the pentagon).