5.1 Triangle Inequality Advanced

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 two sides of a triangle are 10 and 6, what is the range of possible lengths for the third side?

Back

The range of possible lengths for the third side is 4 < x < 16.

Front

What is the relationship between the lengths of the sides and the angles 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

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

Back

The longest side of a triangle is the side with the greatest length compared to the other sides.

Front

In a triangle with sides of lengths 12, 12, and x, what is the range of possible values for x?

Back

The range of possible values for x is 0 < x < 24.

Front

What is the significance of the order of angles in a triangle?

Back

The order of angles in a triangle indicates their relative sizes, with larger angles opposite longer sides.

Front

How can you apply the Triangle Inequality Theorem to real-world problems?

Back

You can use the Triangle Inequality Theorem to determine if three lengths can form a triangle, which is useful in construction and design.

Front

What is the formula to find the range of the third side in a triangle given two sides a and b?

Back

The range of the third side c is given by |a - b| < c < a + b.

Front

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

Back

The relationship is that the larger the side, the larger the angle opposite that side.

Front

If a triangle has sides of lengths 5, 7, and 12, does it satisfy the Triangle Inequality Theorem?

Back

No, it does not satisfy the Triangle Inequality Theorem because 5 + 7 is not greater than 12.