Hinge Theorem - Practice

Front

What is the Hinge Theorem?

Back

The Hinge Theorem states that if two triangles have two sides equal in 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 triangle ABC has sides AB = 5 cm, AC = 7 cm, and angle A = 60°, which side is longer: BC or AC?

Back

BC is longer than AC because angle A is larger than the angle opposite side AC.

Front

In triangle XYZ, if XY = 8 cm, XZ = 10 cm, and angle Y is larger than angle Z, which side is the longest?

Back

XZ is the longest side because it is opposite the largest angle.

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, which means all corresponding sides and angles are equal.

Front

If two sides of a triangle are equal, what can be said about the angles opposite those sides?

Back

The angles opposite the equal sides are also equal.

Front

In triangle DEF, if DE = 12 cm, DF = 15 cm, and angle E is larger than angle F, which side is longer?

Back

DF is longer than DE because it is opposite the larger angle.

Front

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

Back

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

Front

If triangle GHI has GH = 9 cm, GI = 12 cm, and angle H is the largest angle, which side is the longest?

Back

Side II is the longest side because it is opposite the largest angle.

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 sides opposite the angles.

Front

If two triangles share a side and have two equal angles, what can be concluded about their sides?

Back

The sides opposite the equal angles will also be equal.