# Creating Triangles: How Many Can You Make?

• MHB
• MichaelLiu
In summary, there are three ways to form a triangle with the given dots: one dot at the corner, one from the row of seven, and one from the column of four; two dots on the row of seven, and one on the column of four; or one dot on the row of seven, and two on the column of four. When counting the number of triangles in each way, we get a total of 154 triangles.
MichaelLiu
How many triangles can be made given the following dots?

Thanks a lot!

Apart from the location at the top left corner of the diagram, there are seven locations on the horizontal row, and four locations on the vertical column. There are three ways to place dots on three of these locations to form a triangle:

First way: one dot at the corner, one from the row of seven, and one from the column of four;
Second way: two dots on the row of seven, and one on the column of four (as in the above diagram);
Third way: one dot on the row of seven, and two on the column of four.

Can you count the number of triangles formed in each of these three ways?

Hey @Opalg ! Thank you for your response!

Would this be the correct answer?

First way:
7C1 x 4C1 = 28

Second way:
7C2 x 4C1 = 84

Third way:
7C1 x 4C2 = 42

28 + 84 + 42 = 154 triangles

MichaelLiu said:
Hey @Opalg ! Thank you for your response!

Would this be the correct answer?

First way:
7C1 x 4C1 = 28

Second way:
7C2 x 4C1 = 84

Third way:
7C1 x 4C2 = 42

28 + 84 + 42 = 154 triangles
Looks good to me. (Yes)

## 1. How many triangles can be made using three line segments?

There are infinitely many triangles that can be made using three line segments. This is because the length of the line segments and the angles between them can vary, resulting in a different triangle each time.

## 2. What is the minimum number of line segments needed to create a triangle?

At least three line segments are needed to create a triangle. This is because a triangle is a polygon with three sides.

## 3. Can any three line segments form a triangle?

No, not all combinations of three line segments can form a triangle. The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This is known as the Triangle Inequality Theorem.

## 4. Are there any special types of triangles that can be made?

Yes, there are several special types of triangles that can be made, such as equilateral, isosceles, and scalene triangles. These types are determined by the length of the sides and the angles between them.

## 5. Can a triangle be created with three right angles?

No, a triangle cannot have three right angles. The sum of the interior angles of a triangle is always 180 degrees, so it is not possible for all three angles to be 90 degrees.

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