Hinge Theorem and Inequalities

The video tutorial explains how to use the hinge theorem and its converse to solve inequalities involving triangles. It begins with an introduction to the hinge theorem, followed by a detailed explanation of applying its converse to solve inequalities. The tutorial then demonstrates solving inequalities using congruent sides and angles, concluding with a summary of the key points discussed.

What is the primary focus of the hinge theorem?

• Properties of polygons

• Properties of quadrilaterals

• Properties of triangles

• Properties of circles

What does the hinge theorem help to determine in a triangle?

• The area of the triangle

• The congruence of triangles

• The perimeter of the triangle

• The relationship between angles and opposite sides

What does the converse of the hinge theorem help determine?

• The congruence of angles

• The sum of angles in a triangle

• The congruence of sides

• The relationship between angles and opposite sides

In the context of the hinge theorem, what does the reflexive property imply?

• A side is equal to itself

• An angle is equal to itself

• A triangle is equal to itself

• A side is equal to another side

What is the significance of the included angles in the hinge theorem?

• They determine the congruence of triangles

• They determine the relationship between sides

• They determine the sum of angles

• They determine the area of the triangle

What inequality is derived using the hinge theorem in the first example?

• X + 18 > 52

• X + 18 < 52

• X - 18 < 52

• X - 18 > 52

How does the hinge theorem relate to the size of angles?

• Larger angles are opposite larger sides

• Smaller angles are opposite larger sides

• Angles are unrelated to side sizes

• Larger angles are opposite smaller sides

What is the solution to the inequality X + 18 < 52?

• X = 34

• X ≤ 34

• X > 34

• X < 34

In the second problem, what is the relationship between the smallest side and the angle?

• The smallest side is equal to the largest angle

• The smallest side is equal to the smallest angle

• The smallest side is opposite the smallest angle

• The smallest side is opposite the largest angle

What inequality is derived in the second problem?

• X > 3X - 8

• X < 3X - 8

• X = 3X - 8

• X ≥ 3X - 8