Triangle Inequality Theorem (Section 5-5)

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 a triangle has sides of lengths a, b, and c, what inequalities must hold true?

Back

The inequalities that must hold true are: a + b > c, a + c > b, and b + c > a.

Front

What is the range of possible lengths for the base of an isosceles triangle with legs of length 12?

Back

The range of possible lengths for the base x is: 0 < x < 24.

Front

Given the sides of a triangle as (x + 5), (2x + 22), and (5x - 7), what is the first step to find the possible values for x?

Back

The first step is to apply the Triangle Inequality Theorem to set up inequalities based on the lengths of the sides.

Front

What is the minimum value of x for the triangle with sides (x + 5), (2x + 22), and (5x - 7)?

Back

To find the minimum value of x, solve the inequality (x + 5) + (2x + 22) > (5x - 7).

Front

What is the maximum value of x for the triangle with sides (x + 5), (2x + 22), and (5x - 7)?

Back

To find the maximum value of x, solve the inequality (5x - 7) + (x + 5) > (2x + 22).

Front

If the lengths of two sides of a triangle are 8 and 10, what is the range of possible lengths for the third side?

Back

The range for the third side x is: 2 < x < 18.

Front

What happens if the Triangle Inequality Theorem is not satisfied?

Back

If the Triangle Inequality Theorem is not satisfied, the lengths cannot form a triangle.

Front

How can you determine if three lengths can form a triangle?

Back

Check if the sum of any two lengths is greater than the third length for all three combinations.

Front

What is an isosceles triangle?

Back

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