Triangle Inequalities and Hinge Theorem Review

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

How do you determine the longest side of a triangle?

Back

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

Front

If two sides of a triangle are 8 cm and 5 cm, what is the range of possible lengths for the third side?

Back

The range for the third side is: 3 cm < x < 13 cm.

Front

What does the Hinge Theorem state?

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

If side lengths are 3 cm, 4 cm, and x cm, what is the range for x?

Back

The range for x is: 1 cm < x < 7 cm.

Front

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

Back

In a triangle, larger angles are opposite longer sides.

Front

If angle A is 60 degrees and angle B is 80 degrees, what can you say about the sides opposite these angles?

Back

The side opposite angle B (80 degrees) is longer than the side opposite angle A (60 degrees).

Front

How can you compare two sides of a triangle if you know their opposite angles?

Back

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

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.