Problem:
How many distinct triangles can be drawn using three of the dots below as vertices?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
To make a triangle, select as vertices two dots from one row and one from the other row. To select two dots in the top row, decide which dot is not used. This can be done in three ways. There are also three ways to choose one dot to use from the bottom row. So there are triangles with two vertices in the top row and one in the bottom. Similarly, there are nine triangles with one vertex in the top row and two in the bottom. This gives a total of triangles.
Note: Can you find the four noncongruent triangles?
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions