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

State 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

What is the relationship between angles and opposite sides in a triangle?

Back

In a triangle, the larger angle is opposite the longer side, and the smaller angle is opposite the shorter side.

Front

If two angles of a triangle are equal, what can be said about the lengths of the sides opposite those angles?

Back

If two angles of a triangle are equal, then the sides opposite those angles are also equal in length.

Front

What is the range of possible lengths for the third side of a triangle with sides of lengths 8 and 10?

Back

The range of possible lengths for the third side is 2 < x < 18.

Front

How do you determine if a triangle can exist with given side lengths?

Back

A triangle can exist with given side lengths if the sum of the lengths of any two sides is greater than the length of the third side.

Front

What inequality can be formed if angle 1 is less than angle 2?

Back

If angle 1 is less than angle 2, then the side opposite angle 1 is shorter than the side opposite angle 2.

Front

If two sides of a triangle are 5 and 7, what is the maximum length of the third side?

Back

The maximum length of the third side is 11 (5 + 7 - 1).

Front

What is the minimum length of the third side if two sides are 5 and 7?

Back

The minimum length of the third side is 2 (7 - 5 + 1).

Front

If angle A is 30 degrees and angle B is 60 degrees, which side is longer?

Back

The side opposite angle B is longer than the side opposite angle A.