Hinge Theorem

Front

What is the Hinge Theorem?

Back

The Hinge Theorem states that if two triangles have two sides of one triangle equal to two sides of another triangle, and the included angle of the first triangle is larger than the included angle of the second triangle, then the side opposite the larger angle in the first triangle is longer than the side opposite the larger angle in the second triangle.

Front

How does the Hinge Theorem apply to comparing lengths of sides in triangles?

Back

The Hinge Theorem can be used to determine which side of two triangles is longer based on the lengths of the other two sides and the included angles.

Front

If triangle ABC has sides AB = 5, AC = 7, and angle A = 60°, and triangle DEF has sides DE = 5, DF = 8, and angle D = 30°, which side is longer?

Back

DF is longer than AC because angle D is smaller than angle A, and DF is opposite the larger angle.

Front

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

Back

In triangles, the larger the angle, the longer the side opposite to it.

Front

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

Back

The side opposite the larger angle in the triangle with the larger included angle will be longer.

Front

In triangle XYZ, if XY = 10, XZ = 12, and angle X = 70°, and in triangle PQR, if PQ = 10, PR = 15, and angle P = 50°, which side is longer?

Back

PR is longer than XZ because angle P is smaller than angle X, and PR is opposite the larger angle.

Front

What is the converse of the Hinge Theorem?

Back

The converse of the Hinge Theorem states that if two triangles have two sides equal and the side opposite the angle in one triangle is longer, then the angle in that triangle is larger.

Front

How can the Hinge Theorem be used in real-life applications?

Back

The Hinge Theorem can be used in fields such as engineering and architecture to determine structural integrity and design.

Front

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

Back

Given two triangles with sides 6, 8, and angles 45° and 60°, you can conclude that the side opposite the 60° angle is longer.

Front

If triangle ABC has sides AB = 9, AC = 12, and angle A = 40°, and triangle DEF has sides DE = 9, DF = 10, and angle D = 30°, which side is longer?

Back

AC is longer than DF because angle A is larger than angle D.