Triangle Inequalities

Front

Can the sides of a triangle have lengths 3, 4, and 9?

Back

No, because the sum of the lengths of the two shorter sides (3 + 4 = 7) must be greater than the length of the longest side (9).

Front

Does a triangle with these side lengths exist: 15, 12, 9?

Back

Yes, because the sum of the lengths of any two sides (15 + 12 > 9, 15 + 9 > 12, 12 + 9 > 15) is greater than the length of the third side.

Front

Which of the following would NOT work to make a triangle with the two side lengths of 2 and 6? (Options: 6, 7, 5, 4)

Back

4, because the third side must be greater than the difference of the two sides (6 - 2 = 4) and less than their sum (2 + 6 = 8).

Front

The smallest angle would be located where in a triangle?

Back

Across from the smallest side.

Front

What is the range of values the third side of a triangle with sides 2 and 6 could be?

Back

The third side must be greater than 4 and less than 8 (4 < x < 8).

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 one side of a triangle is 10 and another is 15, what is the range of possible lengths for the third side?

Back

The third side must be greater than 5 and less than 25 (5 < x < 25).

Front

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

Back

If the sum of two sides equals the third side, the three points are collinear, and a triangle cannot be formed.

Front

In a triangle with sides 7, 10, and x, what is the range for x?

Back

x must be greater than 3 and less than 17 (3 < x < 17).

Front

What is the relationship between the angles and sides of a triangle?

Back

In a triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.