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

What are the conditions for three lengths to form a triangle?

Back

Three lengths a, b, and c can form a triangle if the following conditions are met: a + b > c, a + c > b, and b + c > a.

Front

What type of triangle has two equal sides?

Back

An Isosceles triangle has two equal sides.

Front

What type of triangle has all sides of different lengths?

Back

A Scalene triangle has all sides of different lengths.

Front

What type of triangle has one angle that measures 90 degrees?

Back

A Right triangle has one angle that measures 90 degrees.

Front

If two sides of a triangle measure 8 and 12, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 4 and less than 20, so the range is 4 < x < 20.

Front

Which of the following lengths cannot represent the sides of a triangle: 28, 30, 58?

Back

The lengths 28, 30, and 58 cannot represent the sides of a triangle because they do not satisfy the Triangle Inequality Theorem.

Front

What is a Right Isosceles triangle?

Back

A Right Isosceles triangle is a triangle that has a right angle (90 degrees) and two sides of equal length.

Front

How do you identify the longest side of a triangle?

Back

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

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.