Exploring the Triangle Inequality Theorem

What does the Triangle Inequality Theorem state?

• Any three line segments can form a triangle.

• Not every group of three line segments can form a triangle.

• The theorem applies only to isosceles triangles.

• Only right triangles follow the theorem.

What must be true for three line segments to form a triangle?

• The sum of any two segments must be equal to the third side.

• The sum of any two segments must be exactly half of the third side.

• The sum of any two segments must be less than the third side.

• The sum of any two segments must be greater than the third side.

How is the relationship of the Triangle Inequality Theorem written mathematically?

• a + b < c

• a + b > c

• a + b = c

• a + b ≤ c

Given line segments of lengths 7 cm, 5 cm, and 1 cm, can they form a triangle?

• Yes, because 7 + 5 > 1

• No, because 5 + 1 is not greater than 7

• Yes, because 7 + 1 > 5

• No, because 7 + 5 is not greater than 1

Which of the following sets of line segments can form a triangle?

• 3 cm, 4 cm, 5 cm

• 2 cm, 2 cm, 5 cm

• 1 cm, 1 cm, 3 cm

• 3 cm, 4 cm, 8 cm

What is the easiest way to check if three line segments can form a triangle?

• Check if the longest side is equal to the sum of the other two sides.

• Check if the longest side is exactly half of the sum of the other two sides.

• Check if the longest side is less than the sum of the other two sides.

• Check if the longest side is greater than the sum of the other two sides.

In the example with line segments of 3 cm, 4 cm, and 5 cm, why can they form a triangle?

• Because 3 + 4 is equal to 5

• Because 3 + 4 is greater than 5

• Because 4 + 5 is less than 3

• Because 5 + 3 is less than 4

How is the Triangle Inequality Theorem used in GPS triangulation?

• To measure the height of satellites.

• To calculate the distance between two points on Earth.

• To find the area of a triangle.

• To determine the speed of a moving object.

What does GPS triangulation involve?

• Using four satellites to form a square.

• Using three satellites to form a triangle.

• Using one satellite to measure distance.

• Using two satellites to form a line.

What is the purpose of triangulation in GPS?

• To determine the depth of the ocean.

• To find the exact location of a point.

• To measure the height of a building.

• To calculate the speed of a vehicle.