The video tutorial explains the hinge theorem, which applies when two triangles have two congruent sides and an included angle. The theorem states that if the included angle of one triangle is larger than that of another, the side opposite the larger angle is longer. The tutorial uses an example with angles of 90 and 80 degrees to demonstrate this concept, concluding that the side opposite the 90-degree angle is longer.

What is a necessary condition for the hinge theorem to be applicable?

• Two equal sides and a non-included angle

• Two equal angles and a non-included side

• Two congruent sides and an included angle

• Two congruent angles and a side

In the hinge theorem, if one triangle has a larger included angle than another, what can be said about the opposite sides?

• The theorem does not apply

• The side opposite the larger angle is longer

• The sides are equal

• The side opposite the larger angle is shorter

Which of the following is true about the hinge theorem?

• It compares the area of two triangles

• It compares the perimeter of two triangles

• It compares side lengths of two different triangles

• It compares angles of two different triangles

What is the relationship between the included angles and the opposite sides in the hinge theorem?

• Included angles do not affect opposite sides

• Larger included angle leads to a shorter opposite side

• Larger included angle leads to a longer opposite side

• Smaller included angle leads to a longer opposite side

What does the hinge theorem help to prove in geometry?

• The equality of angles based on side lengths

• The inequality of side lengths based on angles

• The similarity of two triangles

• The congruence of two triangles