Hinge Theorem

Front

What is the Hinge Theorem?

Back

The Hinge Theorem states that if two triangles have two sides of equal length, the triangle with the larger included angle will have a longer third side.

Front

If two triangles have two equal sides, how can you determine which triangle has the longer third side?

Back

You can determine which triangle has the longer third side by comparing the measures of the included angles; the triangle with the larger included angle has the longer third side.

Front

In triangle ABC, if AB = AC and angle B is larger than angle C, which side is longer?

Back

Side AC is longer than side AB because angle B is larger than angle C.

Front

What is an included angle in a triangle?

Back

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

Front

If triangle DEF has DE = DF and angle E is larger than angle F, what can be said about the lengths of EF and DF?

Back

EF is longer than DF because angle E is larger than angle F.

Front

How does the Hinge Theorem apply to real-world scenarios, such as cranes?

Back

In cranes, the lengths of the arms are fixed, and the angles at which they operate determine the reach; the Hinge Theorem helps in understanding which arm will reach further based on the angles.

Front

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

Back

The relationship is that larger angles correspond to longer opposite sides when two sides are equal.

Front

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

Back

The third side of the triangle with the smaller included angle will be shorter than the third side of the triangle with the larger included angle.

Front

In triangle XYZ, if XY = XZ and angle Y is 30 degrees while angle Z is 60 degrees, which side is longer?

Back

Side XZ is longer than side XY because angle Z is larger than angle Y.

Front

What is the significance of the Hinge Theorem in geometry?

Back

The Hinge Theorem is significant because it provides a method to compare the lengths of sides in triangles based on their angles, which is essential for solving various geometric problems.