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 condition must be satisfied to form a triangle?

Back

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

Front

Can the side lengths 7, 8, and 9 form a triangle?

Back

Yes, because 7 + 8 > 9, 7 + 9 > 8, and 8 + 9 > 7.

Front

Can the side lengths 2, 2, and 4 form a triangle?

Back

No, because 2 + 2 is not greater than 4.

Front

What is the result of applying the Triangle Inequality Theorem to the side lengths 15, 12, and 2?

Back

No, these lengths cannot form a triangle because 15 + 12 > 2, but 15 + 2 is not greater than 12.

Front

What are the side lengths of an equilateral triangle?

Back

All three sides are equal in length.

Front

If a triangle has side lengths of 9, 9, and 9, what type of triangle is it?

Back

It is an equilateral triangle.

Front

What is the minimum length of the third side if two sides of a triangle are 5 and 7?

Back

The minimum length of the third side must be greater than 2 (5 - 7 < x < 5 + 7).

Front

What is the maximum length of the third side if two sides of a triangle are 5 and 7?

Back

The maximum length of the third side must be less than 12 (5 + 7 > x).

Front

Can the side lengths 3, 4, and 8 form a triangle?

Back

No, because 3 + 4 is not greater than 8.