Hinge Theorem and Triangle Properties

The video tutorial explains the hinge theorem using a gate analogy, where the gate represents a triangle's side. It discusses how the theorem applies when two sides of a triangle are congruent to another, but the included angles differ. The video provides examples to illustrate the theorem and its converse, emphasizing the relationship between side lengths and angles. It concludes with problem-solving applications, highlighting the importance of understanding congruent sides and angle measures.

What remains constant in the gate analogy used to explain triangles?

• The material of the gate

• The angle of the gate

• The length of the gate

• The color of the gate

In the hinge theorem, what happens to the side opposite the larger included angle?

• It becomes shorter

• It remains the same

• It becomes longer

• It disappears

Which of the following is necessary for the hinge theorem to apply?

• Triangles must be identical

• Triangles must have congruent sides

• Triangles must be right-angled

• Triangles must be isosceles

In the example with triangles RST and UVW, which angle is larger?

• Angle SRT

• Angle RST

• Angle STU

• Angle UVW

What property is used to show that side EG is congruent to itself?

• Symmetric property

• Reflexive property

• Transitive property

• Associative property

What does the converse of the hinge theorem state about the smaller side?

• It has no angle

• It has the same angle

• It has a smaller angle

• It has a larger angle

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

• The area of the triangle

• The perimeter of the triangle

• The length of the third side

• The color of the sides

When applying the hinge theorem, what is the first step?

• Calculate the perimeter

• Measure all angles

• Find the area of the triangles

• Identify congruent sides

What is the sum of the interior angles of a triangle?

• 360 degrees

• 270 degrees

• 180 degrees

• 90 degrees

In solving inequalities using the hinge theorem, what is the goal?

• To isolate the variable

• To find the area

• To draw the triangle

• To measure the angles