HINGE THEOREM AND ITS CONVERSE

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 third side of the first triangle is longer than the third side of the second triangle.

Front

What is the converse of the Hinge Theorem?

Back

The converse of the Hinge Theorem states that if two triangles have two sides of one triangle equal 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 angle of the first triangle is larger than the included angle of the second triangle.

Front

If triangle ABC has sides AB = 5 cm, AC = 7 cm, and angle A = 60°, what can be said about triangle DEF with sides DE = 5 cm, DF = 7 cm, and angle D?

Back

If angle D is less than 60°, then side EF of triangle DEF will be longer than side BC of triangle ABC.

Tags

CCSS.8.G.A.2

Front

How can you determine if two triangles are congruent using the Hinge Theorem?

Back

You can determine if two triangles are congruent by showing that their corresponding sides are equal and their included angles are equal.

Front

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

Back

In triangles, if one angle is larger than another, the side opposite the larger angle is longer.

Front

If triangle GHI has GH = 8 cm, GI = 6 cm, and angle G = 45°, what can be inferred about triangle JKL with JK = 8 cm, JL = 6 cm, and angle J?

Back

If angle J is greater than 45°, then side KL of triangle JKL will be longer than side HI of triangle GHI.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

What is the significance of the included angle in the Hinge Theorem?

Back

The included angle is significant because it determines the relationship between the lengths of the opposite sides in the two triangles.

Front

Can the Hinge Theorem be applied to non-congruent triangles?

Back

Yes, the Hinge Theorem can be applied to non-congruent triangles to compare the lengths of their sides based on the measures of their included angles.

Front

What is an example of using the Hinge Theorem in a real-world scenario?

Back

An example is in construction, where the Hinge Theorem can help determine the lengths of beams needed based on the angles of support.

Front

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

Back

The triangle with the larger included angle will have a longer third side.