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 3, 4, and 5, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

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

Back

The range is 0 < x < 24.

Front

For a triangle with sides (x + 5), (2x + 22), and (5x - 7), what is the condition for x based on the Triangle Inequality Theorem?

Back

6 < x < 17.

Front

What does it mean if a triangle's sides do not satisfy the Triangle Inequality Theorem?

Back

It means that the lengths cannot form a triangle.

Front

If one side of a triangle is 10 and another is 15, what is the maximum length of the third side?

Back

The maximum length is 24, since 10 + 15 > x.

Front

If the lengths of two sides of a triangle are 8 and 6, what is the minimum length of the third side?

Back

The minimum length is 2, since x > 8 - 6.

Front

What is the significance of the Triangle Inequality Theorem in real-world applications?

Back

It helps in determining whether three lengths can form a triangle, which is crucial in fields like engineering and architecture.

Front

How can you express the Triangle Inequality Theorem mathematically for sides a, b, and c?

Back

The inequalities are: a + b > c, a + c > b, and b + c > a.

Front

What is an isosceles triangle?

Back

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