Triangle Inequality

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

List the conditions for a triangle to exist based on its side lengths.

Back

For a triangle with sides a, b, and c, the following must hold: a + b > c, a + c > b, and b + c > a.

Front

If two sides of a triangle are 10 and 7, what is the range of possible lengths for the third side?

Back

Front

How do you determine the order of angles in a triangle based on their measures?

Back

The angles can be ordered from smallest to largest based on the lengths of the opposite sides; the smallest angle is opposite the shortest side.

Front

What type of triangle has one angle greater than 90 degrees?

Back

An obtuse triangle.

Front

What is an isosceles triangle?

Back

An isosceles triangle is a triangle that has at least two sides of equal length.

Front

What is a scalene triangle?

Back

A scalene triangle is a triangle in which all three sides have different lengths.

Front

Can a triangle be formed with side lengths 17, 9, and 30?

Back

No, because 17 + 9 is not greater than 30.

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 sides of a triangle are 5, 12, and 13, what type of triangle is it?

Back