Triangle Inequality and Proof Concepts

The video tutorial covers the triangle inequality theorem, explaining that the sum of any two side lengths of a triangle must be greater than the third side length. It provides examples to demonstrate how to apply the theorem, including calculating possible side lengths and ordering triangle sides based on angle measures. The tutorial concludes with real-world applications and encourages viewers to experiment with creating triangles using different materials.

What is the basic principle of the Triangle Inequality Theorem?

• The sum of all three side lengths of a triangle is equal to zero.

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

• The sum of any two side lengths of a triangle is equal to the third side.

• The sum of any two side lengths of a triangle is less than the third side.

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

• 6 cm, 6 cm, 7.5 cm

• 10.5 cm, 11 cm, 18 cm

• 5 cm, 5 cm, 10 cm

• 6 cm, 6 cm, 18 cm

Why can't segments of lengths 6 cm, 6 cm, and 18 cm form a triangle?

• Because all sides are equal.

• Because 18 + 6 is not greater than 6.

• Because 6 + 18 is not greater than 6.

• Because 6 + 6 is not greater than 18.

According to the Triangle Inequality Theorem, what must be true for three segments to form a triangle?

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

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

• The sum of all three side lengths must be equal.

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

Can a triangle have sides with lengths 4, 6.5, and 11?

• No, because 4 + 6.5 is not greater than 11.

• No, because 11 + 4 is not greater than 6.5.

• Yes, because 6.5 + 11 is greater than 4.

• Yes, because 4 + 6.5 is greater than 11.

What is the range of possible lengths for the third side of a triangle with sides 6 cm and 11 cm?

• Greater than 5 cm and less than 17 cm

• Greater than 6 cm and less than 11 cm

• Greater than 11 cm and less than 17 cm

• Greater than 5 cm and less than 11 cm

In triangle ABD, if angle ABD is 50 degrees, which side is the shortest?

• BD

• AD

• AB

• CD

What is the range of distances from Mason to Austin if the distances from San Antonio to Mason and Austin are 111 miles and 78 miles respectively?

• Greater than 78 miles and less than 111 miles

• Greater than 33 miles and less than 78 miles

• Greater than 33 miles and less than 189 miles

• Greater than 111 miles and less than 189 miles

What is the first step in an indirect proof?

• Assume the desired conclusion is true.

• Ignore the desired conclusion.

• Prove the desired conclusion directly.

• Assume the opposite of the desired conclusion.