5-4 Inequalities in one triangle

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 two sides of a triangle are 5 in and 16 in, what is the range of possible lengths for the third side?

Back

11 in < x < 21 in.

Front

What is the minimum length of the third side if two sides are 12 and 15?

Back

The minimum length is 3 (12 - 15).

Front

What is the maximum length of the third side if two sides are 12 and 15?

Back

The maximum length is 26 (12 + 15).

Front

If a triangle has sides of lengths 5, 7, and x, what is the range of possible values for x?

Back

2 < x < 12.

Front

How do you determine the longest side of a triangle given its side lengths?

Back

The longest side is the one with the greatest numerical value among the three side lengths.

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.

Front

If the angles of a triangle are A, B, and C, how do you order them from smallest to largest based on side lengths?

Back

If a < b < c, then the order of angles is A < B < C.

Front

What is the range of possible lengths for the third side of a triangle with sides 8 in and 10 in?

Back

2 in < x < 18 in.

Front

What is the significance of the Triangle Inequality Theorem in triangle construction?

Back

It ensures that three given lengths can form a triangle.