Triangle Inequality Theorem and Inequalities in Triangles

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 cm and 7 cm, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 2 cm and less than 12 cm (2 < x < 12).

Front

What is the smallest angle in a triangle?

Back

The smallest angle in a triangle is opposite the shortest side.

Front

How do you determine the longest side of a triangle?

Back

The longest side of a triangle is opposite the largest angle.

Front

If the sides of a triangle are 3 cm, 4 cm, and 5 cm, is it a right triangle?

Back

Yes, it is a right triangle because it satisfies the Pythagorean theorem: 3² + 4² = 5².

Front

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

Back

In a triangle, the larger the angle, the longer the side opposite that angle.

Front

Given two sides of lengths 8 cm and 10 cm, what is the maximum length of the third side?

Back

The maximum length of the third side can be 17 cm (8 + 10 - 1).

Front

What is the minimum length of the third side if the other two sides are 6 cm and 9 cm?

Back

The minimum length of the third side must be greater than 3 cm (9 - 6 + 1).

Front

If a triangle has sides of lengths 7 cm, 10 cm, and x cm, what is the range for x?

Back

The range for x is 3 < x < 17.

Front

What is the sum of the angles in any triangle?

Back

The sum of the angles in any triangle is always 180 degrees.