Understanding Triangle Inequality

Why is it impossible to construct a triangle with sides of lengths 6, 3, and 10?

• Because the sum of any two sides is less than the third side.

• Because the sides are too large.

• Because the sides are not integers.

• Because the sides are not in a geometric progression.

What is a Pythagorean triple?

• A set of three numbers that form an isosceles triangle.

• A set of three numbers that are all prime.

• A set of three numbers that satisfy the Pythagorean theorem.

• A set of three numbers that can form an equilateral triangle.

Which of the following is NOT a Pythagorean triple?

• 7, 24, 25

• 8, 15, 17

• 5, 12, 13

• 3, 4, 5

Which of the following sets of lengths can form a triangle?

• 3, 4, 5

• 2, 2, 5

• 1, 1, 3

• 5, 5, 10

What does the triangle inequality theorem state?

• The product of the sides of a triangle is equal to the area.

• The difference between any two sides of a triangle is less than the third side.

• The sum of the angles in a triangle is 180 degrees.

• The sum of any two sides of a triangle is greater than the third side.

If you have lengths 5, 12, and 13, can they form a triangle?

• Yes, because they satisfy the triangle inequality.

• Yes, because they are all even numbers.

• No, because they are not consecutive numbers.

• No, because they do not satisfy the triangle inequality.

How can you verify if three given lengths can form a triangle?

• By checking if the lengths are in arithmetic progression.

• By ensuring the lengths are all prime numbers.

• By ensuring all lengths are even numbers.

• By checking if the sum of any two lengths is greater than the third length.

Why can't lengths 2, 5, and 12 form a triangle?

• Because 2 + 5 is not greater than 12.

• Because 5 + 12 is not greater than 2.

• Because 2 + 12 is not greater than 5.

• Because they are not all odd numbers.

What is the significance of understanding the triangle inequality in geometry?

• It is a fundamental concept for determining if three lengths can form a triangle.

• It helps in calculating the area of triangles.

• It is essential for solving algebraic equations.

• It is used to find the perimeter of triangles.

What should you do if you want to learn more about geometry concepts?

• Ignore them as they are not important.

• Focus only on algebra and calculus.

• Study them thoroughly as they are foundational for future math courses.

• Only learn the concepts that appear in tests.