Triangle Inequalities and Hinge Theorem

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 is the Hinge Theorem?

Back

The Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first triangle is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.

Front

Which side is the longest in a triangle?

Back

The longest side is opposite the largest angle.

Front

How do you determine the smallest angle in a triangle?

Back

The smallest angle is opposite the shortest side.

Front

What set of numbers can represent the lengths of the sides of a triangle?

Back

A set of numbers can represent the lengths of the sides of a triangle if they satisfy the Triangle Inequality Theorem.

Front

What is the range of possible lengths for the third side of a triangle with sides of lengths 12 meters and 7 meters?

Back

The range is 5 < x < 19.

Front

Does a triangle with side lengths 15, 12, and 9 exist?

Back

Yes, it satisfies the Triangle Inequality Theorem.

Front

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

Back

In a triangle, larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

Front

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

Back

It is an isosceles triangle.

Front

What is the sum of the interior angles of a triangle?

Back

The sum of the interior angles of a triangle is always 180 degrees.