Hinge Theorem - Practice

Front

What is the Hinge Theorem?

Back

The Hinge Theorem states that if two triangles have two sides of equal 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 than the side opposite the smaller angle.

Front

How can you determine which of two angles is larger using the Hinge Theorem?

Back

By comparing the lengths of the sides opposite the angles. The angle opposite the longer side is larger.

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 = 50°, which triangle has the larger angle?

Back

Triangle ABC has the larger angle because angle A is opposite the longer side AC.

Front

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

Back

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

Front

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

Back

The third side of the triangle with the larger included angle will be longer than the third side of the other triangle.

Front

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

Back

In triangles, larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

Front

If triangle GHI has sides GH = 10, GI = 12, and angle G = 70°, and triangle JKL has sides JK = 10, JL = 15, and angle J = 60°, which triangle has the longer side opposite the included angle?

Back

Triangle JKL has the longer side opposite the included angle because side JL is longer than side GI.

Front

What is the significance of the Hinge Theorem in real-world applications?

Back

The Hinge Theorem helps in determining distances and angles in fields such as architecture, engineering, and navigation.

Front

How can the Hinge Theorem be applied to solve problems involving distances?

Back

By using the theorem to compare the lengths of sides in triangles formed by points of interest, allowing for the determination of which point is closer or farther away.

Front

If two triangles have one side equal and the other two sides are unequal, how can the Hinge Theorem be used?

Back

The triangle with the larger included angle will have the longer side opposite it.