Triangle Inequality Theorem and Inequalities in Triangles

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

If two sides of a triangle are 7 mm and 4 mm, what is the range of possible lengths for the third side?

Back

More than 3 mm but less than 11 mm.

Front

How do you order the sides of a triangle from greatest to least?

Back

To order the sides, compare their lengths and arrange them from the longest to the shortest.

Front

Given two sides of a triangle measuring 7 ft and 13 ft, what is the range for the third side?

Back

More than 6 ft but less than 20 ft.

Front

Can a triangle exist with side lengths of 15, 12, and 9?

Back

Yes, a triangle with these side lengths can exist.

Front

What is the shortest side in a triangle with sides QP, QM, and MP if QM is the shortest?

Back

QM is the shortest side.

Front

What is the formula to find the range of the third side in a triangle?

Back

If a and b are the lengths of the two sides, the range for the third side c is: |a - b| < c < a + b.

Front

What does it mean if a triangle is classified as 'scalene'?

Back

A scalene triangle has all sides of different lengths.

Front

What does it mean if a triangle is classified as 'isosceles'?

Back

An isosceles triangle has at least two sides of equal length.

Front

What does it mean if a triangle is classified as 'equilateral'?

Back

An equilateral triangle has all three sides of equal length.