Triangle Inequality Theorem and Inequalities in Triangles

Front

What is the Triangle Inequality Theorem?

Back

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

Front

If two sides of a triangle are 7 ft and 13 ft, what is the range of possible lengths for the third side?

Back

More than 6 ft but less than 20 ft.

Front

How do you determine the shortest side in a triangle?

Back

The shortest side is the one with the least length among the three sides.

Front

Given two sides of a triangle measuring 7 mm and 4 mm, what is the range for the third side?

Back

More than 3 mm but less than 11 mm.

Front

In triangle ABC, if AB = 10 inches and BC = 17 inches, what could be the length of side AC?

Back

16 inches.

Front

What is the longest side in a triangle?

Back

The longest side is the one with the greatest length among the three sides.

Front

If the sides of a triangle are 5 cm, 12 cm, and x cm, what is the inequality that x must satisfy?

Back

x must be greater than 7 cm and less than 17 cm.

Front

What is the relationship between the sides of a triangle?

Back

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

Front

If one side of a triangle is 8 inches and another is 15 inches, what is the maximum length of the third side?

Back

The maximum length of the third side is less than 23 inches.

Front

What happens if the sum of two sides equals the third side?

Back

The triangle cannot exist; it is a degenerate triangle.