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

If the lengths of two sides of a triangle are 3 and 4, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 1 (3 - 4) and less than 7 (3 + 4). So, the range is (1, 7).

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

Write an inequality relating the measure of angle 1 to the measure of angle 2 if angle 1 is larger.

Back

Front

Which side is the longest in a triangle with sides 5, 12, and 13?

Back

The longest side is 13.

Front

Write an inequality relating AB to DE if AB is shorter than DE.

Back

Front

If a triangle has sides of lengths 7, 10, and 12, does it satisfy the Triangle Inequality Theorem?

Back

Yes, it satisfies the theorem because 7 + 10 > 12, 7 + 12 > 10, and 10 + 12 > 7.

Front

Can a triangle have sides of lengths 2, 2, and 5?

Back

No, it cannot because 2 + 2 is not greater than 5.

Front

What is the relationship between the angles and sides in a triangle according to the Hinge Theorem?

Back

The larger the angle, the longer the opposite side.

Front

If angle 1 measures 60 degrees and angle 2 measures 40 degrees, write an inequality relating them.

Back