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, then the side opposite the larger angle is longer.

Front

If two triangles have two equal sides, what can be said about the angles opposite those sides?

Back

The angles opposite the equal sides are also equal.

Front

In triangle ABC, if AB = AC and angle B is larger than angle C, which side is longer?

Back

Side AC is longer than side AB.

Front

What does it mean for an angle to be larger in the context of the Hinge Theorem?

Back

A larger angle means that the side opposite that angle is longer compared to the side opposite a smaller angle when the other two sides are equal.

Front

If angle 1 is larger than angle 2 in two triangles with two equal sides, what can be concluded about the sides opposite those angles?

Back

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

Front

In the context of the Hinge Theorem, what is the relationship between angles and sides?

Back

The relationship is that larger angles correspond to longer opposite sides when two sides are equal.

Front

If triangle DEF has DE = DF and angle E is larger than angle F, which side is longer?

Back

Side DF is longer than side DE.

Front

How can the Hinge Theorem be applied to compare two triangles?

Back

By comparing the lengths of the sides and the measures of the angles, one can determine which triangle is larger based on the Hinge Theorem.

Front

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

Back

The included angle is crucial because it determines the relationship between the lengths of the opposite sides when two sides are equal.

Front

If two triangles have two equal sides and one triangle has a larger included angle, what can be inferred about the third side?

Back

The third side of the triangle with the larger included angle will be longer.