Hinge Theorem & Converse

Front

Definition of Hinge Theorem

Back

If two triangles have two sides congruent to each other, but one of the included angles is wider, that means that the third side of that triangle is longer.

Front

Definition of Converse of Hinge Theorem

Back

If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first triangle is longer than the third side of the second triangle, then the included angles in the first triangle are larger than the included angle in the second triangle.

Front

Symbol for comparing angles: m∠ABC ___ m∠DEF

Back

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Front

Symbol for comparing segments: AD ___ CD

Back

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Front

If two triangles have two sides congruent, what can be said about their included angles if one triangle has a longer third side?

Back

The included angle of the triangle with the longer third side is wider.

Front

What does the Hinge Theorem imply about triangle side lengths and angles?

Back

The longer the side opposite an angle, the wider the angle.

Front

If m∠BAC > m∠EDF, what can be inferred about the sides opposite these angles?

Back

The side opposite m∠BAC is longer than the side opposite m∠EDF.

Front

What is the relationship between two triangles with two congruent sides and a wider included angle?

Back

The triangle with the wider included angle has a longer third side.

Front

In the context of the Hinge Theorem, what does 'congruent' mean?

Back

Two sides or angles that are equal in measure.

Front

If triangle ABC has sides AB = 5, AC = 7, and angle A is wider than angle D in triangle DEF with sides DE = 5 and DF = 6, what can be concluded?

Back

Angle A is wider than angle D because side BC is longer than side EF.