Triangle Inequality Theorem

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

Can the numbers 5, 2, and 4 be the measures of the sides of a triangle?

Back

No, because 5 is not less than 2 + 4.

Front

Can the numbers 3, 6, and 2 be the measures of the sides of a triangle?

Back

No, because 6 is not less than 3 + 2.

Front

Can the numbers 3, 10, and 8 be the measures of the sides of a triangle?

Back

Yes, because 3 + 8 > 10, 3 + 10 > 8, and 10 + 8 > 3.

Front

Can the numbers 2, 15, and 16 be the measures of the sides of a triangle?

Back

Yes, because 2 + 15 > 16, 2 + 16 > 15, and 15 + 16 > 2.

Front

Can the numbers 5, 8, and 4 be the measures of the sides of a triangle?

Back

No, because 8 is not less than 5 + 4.

Front

What is the first condition of the Triangle Inequality Theorem?

Back

The sum of the lengths of the two shorter sides must be greater than the length of the longest side.

Front

What is an example of a set of numbers that can form a triangle?

Back

The numbers 7, 10, and 5 can form a triangle because 7 + 5 > 10, 7 + 10 > 5, and 10 + 5 > 7.

Front

What is an example of a set of numbers that cannot form a triangle?

Back

The numbers 1, 2, and 3 cannot form a triangle because 1 + 2 is not greater than 3.

Front

What happens if one side is equal to the sum of the other two sides?

Back

If one side is equal to the sum of the other two sides, the three points are collinear, and they do not form a triangle.