Triangle Inequality 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

Will the segments of lengths 3, 4, and 8 form a triangle?

Back

No, because 3 + 4 is not greater than 8.

Front

Find the range of possible values for x if the sides are 2, x, and 6.

Back

Front

Find the range of possible values for x if the sides are 5, x, and 10.

Back

Front

Identify the shortest side if the sides are 7, 5, and 9.

Back

5 is the shortest side.

Front

Identify the smallest angle if the sides are 8, 6, and 10.

Back

The smallest angle is opposite the shortest side, which is 6.

Front

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

Back

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

Front

If two sides of a triangle are 7 and 10, what is the range for the third side?

Back

Front

What is the significance of the Hinge Theorem in triangle comparisons?

Back

The Hinge Theorem helps determine which triangle is larger based on the lengths of two sides and the included angle.