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 help us determine in triangles?

• The congruence of all sides

• The area of the triangle

• The perimeter of the triangle

• The relationship between angles and opposite sides

In the converse of the Hinge Theorem, what is compared to determine the larger angle?

• The base of the triangles

• The height of the triangles

• The length of the sides opposite the angles

• The sum of all angles

What does the Hinge Theorem imply if two triangles have identical side lengths?

• The triangles have different perimeters

• The triangles are similar

• The angles are different

• The triangles are congruent

How does the Hinge Theorem relate to the concept of congruent triangles?

• It determines the area of congruent triangles

• It helps compare angles based on side lengths

• It shows that angles are always equal

• It proves triangles are congruent

What happens to the angles if the side lengths in the Hinge Theorem are equal?

• The angles are different

• The angles are congruent

• The angles are complementary

• The angles are supplementary

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

• Both angles are equal

• Angle F

• Cannot be determined

• Angle A

What is the significance of the shared side in Example 2?

• It is used to apply the reflexive property

• It is irrelevant to the theorem

• It determines the area of the triangles

• It makes the triangles identical

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

• Side DC

• Side DB

• Side BC

• Side AB

In Example 3, what is the key difference between the two triangles?

• The length of the shared side

• The angles are congruent

• The triangles are identical

• The side lengths opposite the angles

Which angle is larger in Example 3 based on the side lengths?

• Cannot be determined

• Both angles are equal

• Angle ATC

• Angle SAT