Understanding the Hinge Theorem

In this video, Justin introduces the hinge theorem and its converse, explaining how they relate to triangle properties. The lesson includes visual aids, such as a door analogy, to help understand the theorem. Two example problems are solved, demonstrating the application of the hinge theorem and its converse to find missing values in triangles.

What is the primary focus of the hinge theorem?

• The relationship between angles and sides in a single triangle.

• The relationship between two triangles with congruent sides.

• The relationship between the sides of a square.

• The relationship between the angles of a quadrilateral.

How does the hinge theorem help in understanding triangles?

• It helps in comparing the third side of two triangles with congruent sides.

• It helps in determining the congruence of two triangles.

• It helps in calculating the area of a triangle.

• It helps in finding the perimeter of a triangle.

What analogy is used to explain the hinge theorem?

• A sliding drawer.

• A window opening.

• A door hinge.

• A rotating wheel.

In the door analogy, what does the door frame represent?

• The base of the triangle.

• The congruent sides of the triangle.

• The included angle of the triangle.

• The third side of the triangle.

What is the importance of the door analogy in understanding the hinge theorem?

• It helps in visualizing the relationship between angles and sides.

• It helps in calculating the area of triangles.

• It helps in proving the congruence of triangles.

• It helps in finding the perimeter of triangles.

What does the converse of the hinge theorem allow us to determine?

• The congruence of two triangles.

• The perimeter of a triangle.

• Which angle is larger based on the third side's length.

• The area of a triangle.

What is the key difference between the hinge theorem and its converse?

• The hinge theorem deals with angles, while the converse deals with sides.

• The hinge theorem deals with sides, while the converse deals with angles.

• The hinge theorem is about quadrilaterals, while the converse is about triangles.

• The hinge theorem is about congruence, while the converse is about similarity.

In the first example, what is the initial step to solve the problem using the hinge theorem?

• Identify the congruent angles.

• Identify the congruent sides.

• Calculate the area of the triangles.

• Determine the perimeter of the triangles.

What inequality is derived from the first example problem using the hinge theorem?

• x + 1 > 10

• x + 1 < 10

• x + 1 = 10

• x + 1 ≥ 10

In the first example, what additional condition is considered for the inequality?

• x + 1 must be less than 0.

• x + 1 must be equal to 0.

• x + 1 must be greater than 10.

• x + 1 must be greater than 0.