Triangle Inequality Theorem 11.19.24

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 one side of a triangle is the longest, what must be true about the other two sides?

Back

The sum of the lengths of the two shorter sides must be greater than the length of the longest side.

Front

Can the side lengths 3, 5, and 8 form a triangle? Why or why not?

Back

No, because 3 + 5 is not greater than 8.

Front

Given side lengths of 7 yd, 8 yd, and 9 yd, can these form a triangle?

Back

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

Front

In triangle ABC, if AB = 10 inches and BC = 17 inches, what is a possible length for AC?

Back

AC must be greater than 7 inches and less than 27 inches. A possible length is 16 inches.

Front

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

Back

The minimum length must be greater than 2 (5 - 7) and less than 12 (5 + 7).

Front

What is the maximum length of a side in a triangle if the other two sides are 4 and 6?

Back

The maximum length must be less than 10 (4 + 6).

Front

If a triangle has sides of lengths 2, 2, and 5, can it exist?

Back

No, because 2 + 2 is not greater than 5.

Front

What is the relationship between the sides of a triangle and the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem provides the necessary conditions for three lengths to form a triangle.

Front

If the sides of a triangle are 8, 15, and x, what is the range of possible values for x?

Back

x must be greater than 7 (8 - 15) and less than 23 (8 + 15).