Triangle Inequality Theorem

According to the Triangle Inequality Theorem, which of the following statements is true for any triangle?

• The sum of the lengths of any two sides is less than the length of the third side.

• The sum of the lengths of any two sides is greater than the length of the third side.

• The product of the lengths of any two sides is equal to the length of the third side.

• The difference between the lengths of any two sides is equal to the length of the third side.

In a triangle with side lengths 5, 7, and 10 units, which of the following statements is true?

• It is not a triangle.

• The triangle is a right triangle.

• The triangle is an equilateral triangle.

• The triangle satisfies the Triangle Inequality Theorem.

If a triangle has side lengths of 3, 4, and 9 units, which of the following statements is true?

• The triangle is acute.

• The triangle is obtuse.

• The triangle is right-angled.

• The triangle does not satisfy the Triangle Inequality Theorem.

Which of the following sets of side lengths could form a triangle according to the Triangle Inequality Theorem?

• 3, 4, 9

• 6, 10, 15

• 2, 5, 12

• 5, 6, 12

If a triangle has side lengths 6, 8, and 12 units, which of the following statements is true?

• The triangle is equilateral.

• The triangle is isosceles.

• The triangle is scalene.

• The triangle satisfies the Triangle Inequality Theorem.

Which of the following sets of side lengths could form a triangle according to the Triangle Inequality Theorem?

• 1, 2, 3

• 4, 5, 6

• 3, 3, 6

• 2, 3, 6

Which of the following sets of side lengths could NOT form a triangle according to the Triangle Inequality Theorem?

• 1, 2, 3

• 4, 5, 6

• 7, 8, 9

• 10, 11, 12

The set of side lengths 10, 10, 12 can form a triangle.

• True

• False

The set of side lengths 10, 10, 12 CAN NOT form a triangle.

• True

• False

Which of the following set of side lengths can form a right triangle?

• 2, 3, 4

• 6, 8, 10

• 5, 5, 5

• 2, 4, 6