Hinge Theorem

Front

What is the Hinge Theorem?

Back

The Hinge Theorem states that if two triangles have two sides of equal length and the included angle of one triangle is larger than the included angle of the other triangle, then the side opposite the larger angle is longer than the side opposite the smaller angle.

Front

Why is it called the Hinge Theorem?

Back

It is called the Hinge Theorem because the vertex of the angle acts like a hinge to open the triangle.

Front

What is the range of possible measures for the third side of a triangle with sides measuring 9 and 6?

Back

Front

What is the range of possible measures for the third side of a triangle with sides measuring 10 and 7?

Back

Front

Which of the following side lengths can form a triangle: 1, 2, 3 or 5, 7, 8 or 6, 6, 14 or 80, 20, 50?

Back

The side lengths that can form a triangle are 5, 7, 8.

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 8 and 5, what is the range for the third side?

Back

Front

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

Back

To determine if three lengths can form a triangle, check if the sum of the lengths of any two sides is greater than the length of the third side.

Front

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

Back

According to the Hinge Theorem, if two triangles have two sides of equal length, the triangle with the larger included angle will have the longer opposite side.

Front

What is the significance of the included angle in the Hinge Theorem?

Back

The included angle is significant because it determines the relative lengths of the opposite sides in the two triangles being compared.