Triangle Inequality Theorem

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that in any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

If one angle of a triangle is larger than another, what can be said about the lengths of the sides opposite those angles?

Back

The side opposite the larger angle is longer than the side opposite the smaller angle.

Front

How do you order the angles of a triangle from smallest to largest?

Back

Order the angles based on their measures; the smallest angle corresponds to the shortest side, and the largest angle corresponds to the longest side.

Front

How do you order the sides of a triangle from longest to shortest?

Back

Order the sides based on their lengths; the longest side corresponds to the largest angle, and the shortest side corresponds to the smallest 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.

Front

If a triangle has sides of lengths 3, 4, and 5, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

What is the sum of the angles in any triangle?

Back

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

Front

If two sides of a triangle are equal, what type of triangle is it?

Back

It is an isosceles triangle.

Front

What is an equilateral triangle?

Back

An equilateral triangle is a triangle in which all three sides are of equal length and all three angles are equal, each measuring 60 degrees.

Front

How can you determine if a triangle is a right triangle using the sides?

Back

If the square of the length of the longest side is equal to the sum of the squares of the lengths of the other two sides, then it is a right triangle (Pythagorean theorem).