HONORS Triangle Inequalities & Hinge Theorem

Front

What is the Triangle Inequality Theorem?

Back

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

Front

If two sides of a triangle are 5 and 10, what is the range of possible lengths for the third side?

Back

The third side must be greater than 5 - 10 (which is not possible) and less than 5 + 10, so the range is 5 < third side < 15.

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

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

Back

In a triangle, the larger the angle, the longer the opposite side.

Front

If a triangle has sides of lengths 7, 10, and x, what is the range of possible values for x?

Back

The range is |7 - 10| < x < 7 + 10, so 3 < x < 17.

Front

What is the smallest angle in a triangle with sides 3, 4, and 5?

Back

The smallest angle is opposite the shortest side, which is 3.

Front

How do you determine if three lengths can form a triangle?

Back

Use the Triangle Inequality Theorem: the sum of any two sides must be greater than the third side.

Front

If two sides of a triangle are 8 and 15, what is the maximum length of the third side?

Back

The maximum length of the third side is 8 + 15 = 23.

Front

What is the minimum length of the third side if two sides are 8 and 15?

Back

The minimum length of the third side is |8 - 15| = 7.

Front

In triangle ABC, if angle A is 30 degrees and angle B is 60 degrees, which angle is the largest?

Back

Angle C is the largest because the sum of angles in a triangle is 180 degrees, so angle C = 180 - 30 - 60 = 90 degrees.