Understanding the Hinge Theorem

The video tutorial explains the hinge theorem, which states that if two triangles have two congruent sides but different included angles, the side opposite the larger angle is longer. The converse of the hinge theorem is also discussed, where given three side lengths, the larger angle is opposite the longer side. Examples are provided to illustrate these concepts, including comparing angles and sides in triangles with shared sides.

What does the hinge theorem primarily relate in a triangle?

• The area of the triangle

• The sum of all angles

• The relationship between angles and opposite sides

• The congruence of all sides

How does the hinge theorem help in understanding triangle properties?

• By comparing the perimeters

• By relating angles to opposite sides

• By determining the area

• By proving congruence

In the context of the hinge theorem, what does a larger angle indicate?

• A smaller opposite side

• A larger opposite side

• Equal opposite sides

• No relation to the opposite side

In the converse of the hinge theorem, what is used to determine the larger angle?

• The sum of the angles

• The congruence of the angles

• The length of the sides opposite the angles

• The perimeter of the triangle

What happens to the angles if the side lengths are equal in the hinge theorem?

• The angles are congruent

• The angles are different

• The angles are supplementary

• The angles are complementary

In Example 1, which angle is larger based on the side lengths provided?

• Angle F

• Cannot be determined

• Angle A

• Both angles are equal

What is the key difference in the setup of Example 2 compared to Example 1?

• The triangles are not congruent

• The triangles share a side

• The triangles are equilateral

• The triangles have different perimeters

In Example 2, which side is longer due to the angle comparison?

• Side AB

• Side BC

• Side AC

• Side DB

In Example 3, what is the relationship between angles SAT and ATC?

• Angle ATC is larger

• Angle SAT is larger

• Both angles are equal

• Cannot be determined

What is the significance of the side lengths in Example 3?

• They determine the congruence of the triangles

• They help compare the angles SAT and ATC

• They are irrelevant to the angle comparison

• They show the triangles are equilateral