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 than the side opposite the smaller angle.

Front

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

Back

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

Front

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

Back

Side BC is longer than side AC.

Front

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

Back

By comparing the lengths of two sides and the included angles, one can determine which triangle has the longer opposite side.

Front

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

Back

In triangles, larger angles are opposite longer sides.

Front

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

Back

Side EF is longer than side DF.

Front

What is the converse of the Hinge Theorem?

Back

If two triangles have two sides of equal length and the side opposite one angle is longer than the side opposite another angle, then the angle opposite the longer side is larger.

Front

In triangle XYZ, if XY = XZ and angle Y is smaller than angle Z, what can be said about side YZ?

Back

Side YZ is shorter than side XZ.

Front

How does the Hinge Theorem help in solving geometric problems?

Back

It allows for the comparison of triangle sides and angles, aiding in determining relationships between different triangles.

Front

What is an example of using the Hinge Theorem in a problem?

Back

Given two triangles with two equal sides, if one triangle has a larger included angle, you can conclude that the side opposite that angle is longer.