Triangle Inequality Theorem Concepts

The video tutorial covers two key inequalities in triangles. The first is the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side. This is demonstrated with examples, including how to check if given side lengths can form a triangle. The second inequality involves the relationship between the sides and angles of a triangle, where the largest side is opposite the largest angle, and so on. A proof is provided to justify this relationship, using an isosceles triangle and the exterior angle theorem.

What is the basic principle of the triangle inequality theorem?

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

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

• The sum of all three sides must be equal.

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

What is the key concept of the triangle inequality theorem?

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

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

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

• The sum of all three sides must be equal.

If a triangle has sides of lengths 3, 4, and 5, does it satisfy the triangle inequality theorem?

• No, because 4 + 5 < 3.

• Yes, because 3 + 5 > 4.

• No, because 3 + 4 < 5.

• Yes, because 3 + 4 > 5.

Why can't the side lengths 13, 3, and 5 form a triangle?

• Because 13 + 3 > 5.

• Because 3 + 5 < 13.

• Because 13 + 5 > 3.

• Because 3 + 13 < 5.

How do you determine if three given side lengths can form a triangle?

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

• Check if the sum of any two sides is equal to the third side.

• Check if the sum of all three sides is equal.

• Check if the sum of any two sides is greater than the third side.

How can you determine the possible values of a side length 'x' in a triangle with sides 13, x, and 7?

• x must be greater than 6 and less than 13.

• x must be greater than 7 and less than 13.

• x must be greater than 6 and less than 20.

• x must be greater than 13 and less than 20.

What is the relationship between the largest side and the largest angle in a triangle?

• The largest side is adjacent to the largest angle.

• The largest side is opposite the intermediate angle.

• The largest side is opposite the largest angle.

• The largest side is opposite the smallest angle.

In a triangle, if angle B is the smallest, which side is opposite to it?

• Any side.

• The intermediate side.

• The largest side.

• The smallest side.

Which angle is opposite the smallest side in a triangle?

• The largest angle.

• The smallest angle.

• Any angle.

• The intermediate angle.

What is the relationship between the intermediate side and angle in a triangle?

• The intermediate side is adjacent to the intermediate angle.

• The intermediate side is opposite the largest angle.

• The intermediate side is opposite the smallest angle.

• The intermediate side is opposite the intermediate angle.