Hinge Theorem

Front

What is the Hinge Theorem?

Back

The Hinge Theorem states that if two triangles have two sides of one triangle congruent to two sides of another triangle, and the included angles are not equal, then the triangle with the larger included angle has the longer third side.

Front

State the conditions for applying the Hinge Theorem.

Back

The conditions for applying the Hinge Theorem are: 1) Two triangles must have two pairs of congruent sides. 2) The included angles must be compared.

Front

If triangle ABC has sides AB = 5 cm, AC = 7 cm, and angle A = 60°, and triangle DEF has sides DE = 5 cm, DF = 7 cm, and angle D = 45°, which triangle has the longer side opposite the included angle?

Back

Triangle ABC has the longer side opposite the included angle because angle A (60°) is greater than angle D (45°).

Front

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

Back

The Hinge Theorem can be used to compare two triangles by analyzing the lengths of their sides in relation to their included angles, allowing us to determine which triangle has the longer side.

Front

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

Back

According to the Hinge Theorem, in triangles, the larger the included angle, the longer the opposite side.

Front

Provide an example of two triangles where the Hinge Theorem can be applied.

Back

Consider triangle GHI with sides GH = 8 cm, GI = 6 cm, and angle G = 70°, and triangle JKL with sides JK = 8 cm, JL = 6 cm, and angle J = 50°. Triangle GHI has a longer side opposite angle G.

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 third sides are unequal, then the angles opposite the longer side is larger.

Front

How does the Hinge Theorem relate to the Law of Sines?

Back

The Hinge Theorem can be seen as a specific case of the Law of Sines, which relates the ratios of the sides of a triangle to the sines of its angles.

Front

What is an included angle in a triangle?

Back

An included angle in a triangle is the angle formed between two sides of the triangle.

Front

If two triangles have two sides equal and the included angles are equal, what can be concluded?

Back

If two triangles have two sides equal and the included angles are equal, then the triangles are congruent.