Triangle Inequality Theorems

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

If a triangle has sides of lengths 9, 40, and 41, does it exist?

Back

Yes, because 9 + 40 > 41, 9 + 41 > 40, and 40 + 41 > 9.

Front

What is the range of possible lengths for the third side of a triangle with sides 17 meters and 12 meters?

Back

5 < x < 29, where x is the length of the third side.

Front

Where is the largest angle of a triangle located?

Back

Across from the longest side.

Front

If one side of a triangle is 20, what can be said about the other two sides?

Back

Both sides must be shorter than 20 to form a triangle.

Front

What is the minimum length of the third side if two sides are 15 and 12?

Back

The minimum length is 3, because 15 - 12 < x.

Front

What is the maximum length of the third side if two sides are 15 and 12?

Back

The maximum length is 27, because 15 + 12 > x.

Front

Can a triangle exist with sides of lengths 15, 12, and 9?

Back

Yes, because 15 + 12 > 9, 15 + 9 > 12, and 12 + 9 > 15.

Front

What does it mean if one side of a triangle is equal to the sum of the other two sides?

Back

It means the triangle is degenerate, and it does not form a proper triangle.

Front

If two sides of a triangle are equal, what type of triangle is it?

Back

It is an isosceles triangle.