Hinge Theorem and Inequalities

The video tutorial explains how to use the hinge theorem and its converse to solve inequalities involving triangles. It demonstrates the process with two examples, highlighting the importance of congruent sides and included angles. The tutorial concludes with a summary of the key points discussed.

What is the primary concept introduced in the video?

• Pythagorean Theorem

• Hinge Theorem

• Cosine Rule

• Sine Rule

What does the Hinge Theorem help to determine in a triangle?

• The relationship between angles and opposite sides

• The length of the hypotenuse

• The perimeter of the triangle

• The area of the triangle

In the first example, what is the inequality set up to solve for X?

• 38 > 3X - 4

• 38 < 3X - 4

• 38 = 3X - 4

• 38 >= 3X - 4

What is the first step in solving the inequality 38 < 3X - 4?

• Subtract 4 from both sides

• Add 4 to both sides

• Multiply both sides by 3

• Divide both sides by 3

After solving the inequality, what is the value of X in the first example?

• X <= 14

• X = 14

• X > 14

• X < 14

What is the key difference in the second example compared to the first?

• Different value of X

• Twist in the application of the Hinge Theorem

• Different triangle type

• Different theorem used

In the second example, what is the inequality set up to solve for X?

• X + 3 >= 3X + 1

• X + 3 > 3X + 1

• X + 3 < 3X + 1

• X + 3 = 3X + 1

What is the first step in solving the inequality X + 3 < 3X + 1?

• Add X to both sides

• Subtract X from both sides

• Multiply both sides by 2

• Divide both sides by 2

After solving the inequality, what is the value of X in the second example?

• X < 1

• X > 1

• X = 1

• X <= 1

What is the significance of the included angle in the Hinge Theorem?

• It is the largest angle in the triangle

• It is the angle between the congruent sides

• It is irrelevant to the theorem

• It determines the area of the triangle