6.6 Hinge Theorem

Front

What is the Hinge Theorem?

Back

The Hinge Theorem states that if two triangles have two sides of one triangle that are equal to two sides of another triangle, and the included angle of the first triangle is greater 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 two triangles share a common side, how does the length of the other sides relate to the angles?

Back

The triangle with the larger angle will have the longer opposite side.

Front

What can be concluded if angle Y is greater than angle M in two triangles?

Back

The side opposite angle Y is longer than the side opposite angle M.

Front

In the context of the Hinge Theorem, what does it mean if AB is greater than DC?

Back

It means that the angle opposite AB is greater than the angle opposite DC.

Front

If two triangles have equal corresponding sides, what can be said about their angles?

Back

The corresponding angles are also equal.

Front

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

Back

The larger the angle, the longer the opposite side.

Front

If EF < FG, what can be inferred about the angles opposite these sides?

Back

The angle opposite EF is less than the angle opposite FG.

Front

What is a necessary condition for applying the Hinge Theorem?

Back

The two triangles must have two pairs of equal sides and the included angles must be compared.

Front

If angle 1 is greater than angle 2, what can be said about the lengths of the sides opposite these angles?

Back

The side opposite angle 1 is longer than the side opposite angle 2.

Front

What does it mean if two triangles are congruent?

Back

It means that all corresponding sides and angles are equal.