What is the Triangle Inequality Theorem - Congruent Triangles

The video tutorial explains the triangle inequality theorem, which helps determine if three sides can form a triangle. It covers examples of equilateral, isosceles, and scalene triangles, demonstrating how the theorem applies to each. The video also provides examples and non-examples to illustrate when three sides do or do not form a triangle, emphasizing that the sum of any two sides must be greater than the third side.

What is the key characteristic of an equilateral triangle?

• One side is longer than the others.

• All sides are different.

• Two sides are equal.

• All sides are equal.

According to the triangle inequality theorem, what must be true for any two sides of a triangle?

• Their sum must be twice the third side.

• Their sum must be equal to the third side.

• Their sum must be less than the third side.

• Their sum must be greater than the third side.

In a scalene triangle, how do the side lengths relate to each other?

• All sides are equal.

• Two sides are equal.

• One side is zero.

• All sides are different.

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

• 2, 2, 5

• 3, 4, 5

• 5, 5, 10

• 1, 2, 3

What must be true for a set of three side lengths to form a triangle?

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

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

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

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

Why can't the side lengths 1, 2, and 8 form a triangle?

• Because 1 + 2 is greater than 8.

• Because 1 + 2 equals 8.

• Because 1 + 2 is less than 3.

• Because 1 + 2 is not greater than 8.

What happens if the sum of two sides of a triangle is equal to the third side?

• It forms a straight line.

• It forms a triangle.

• It forms a square.

• It forms a circle.