Exploring the Triangle Inequality Theorem

What are the given lengths of sides AB and BC in triangle ABC?

• AB = 10, BC = 15

• AB = 12, BC = 17

• AB = 14, BC = 19

• AB = 11, BC = 16

What theorem is used to determine the possible measures of side AC?

• Cosine Rule

• Sine Rule

• Triangle Inequality Theorem

• Pythagorean Theorem

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be:

• Unrelated to the length of the third side

• Greater than the length of the third side

• Less than the length of the third side

• Equal to the length of the third side

If AC is the longest side, what inequality must be true?

• AB + BC > AC

• AB + AC > BC

• AB + BC < AC

• BC + AC > AB

What is the maximum possible length of AC if it is the longest side?

• 12

• 5

• 17

• 29

If BC is the longest side, what inequality must be true?

• AB + AC < BC

• AB + AC > BC

• AB + BC > AC

• BC + AC > AB

What is the minimum possible length of AC if BC is the longest side?

• 5

• 17

• 29

• 12

What is the range of possible values for AC?

• Greater than 12 and less than 29

• Greater than 5 and less than 17

• Greater than 12 and less than 17

• Greater than 5 and less than 29

Which side cannot be the longest side in the given triangle?

• None of the above

• AC

• BC

• AB

What is the final conclusion about the possible measures of AC?

• AC must be greater than 29

• AC must be less than 5

• AC must be greater than 5 but less than 29

• AC can be any length