Triangle Inequality Theorem

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

Given side lengths a, b, and c, what must be true for them to form a triangle?

Back

The following conditions must be satisfied: a + b > c, a + c > b, and b + c > a.

Front

Can a triangle exist with side lengths 0, 11, and 12?

Back

No, a triangle cannot have a side length of 0.

Front

If the side lengths are 15 in., 12 in., and 2 in., can they form a triangle?

Back

No, because 15 + 12 is not greater than 2.

Front

What is an example of side lengths that cannot form a triangle?

Back

Side lengths 28, 30, and 58 cannot form a triangle because 28 + 30 is not greater than 58.

Front

Which of the following sets of lengths can form a triangle: 3 cm, 10 cm, 15 cm?

Back

No, because 3 + 10 is not greater than 15.

Front

What is the significance of the Triangle Inequality Theorem in geometry?

Back

It helps determine whether a set of three lengths can form a triangle, which is fundamental in triangle construction and properties.

Front

How can you determine if three lengths can form a triangle using the Triangle Inequality Theorem?

Back

Check if the sum of the two shorter lengths is greater than the longest length.

Front

What happens if one of the side lengths is equal to the sum of the other two?

Back

The lengths will form a degenerate triangle, which is a straight line, but not a traditional triangle.

Front

What is a degenerate triangle?

Back

A degenerate triangle is a triangle in which the three points are collinear, meaning it has no area.