Understanding Triangle Inequalities

What is the main focus of the hinge theorem in triangle inequalities?

• Comparing angles based on side lengths

• Comparing side lengths based on angles

• Determining congruence of triangles

• Calculating the area of triangles

In the introduction, what activity is mentioned as a precursor to understanding inequalities?

• Calculus problems

• Physics experiments

• Algebraic equations

• Geometer sketch pad activity

Which theorem is also known as the hinge theorem?

• Side-Side-Angle Inequality

• Side-Side-Side Inequality

• Angle-Side-Angle Inequality

• Side-Angle-Side Inequality

What is the result when comparing two triangles using the hinge theorem?

• The triangles are congruent

• The included angle is larger or smaller

• The triangles have equal perimeters

• The triangles have equal areas

In the first example, what is used to determine that angle one is greater than angle two?

• The area of the triangles

• The measure of the angles

• The length of the sides

• The perimeter of the triangles

What is the key concept of the side-side-side inequality?

• Using side lengths to determine area

• Using angles to determine congruence

• Using side lengths to determine angles

• Using angles to determine side lengths

What is the conclusion about EF and ED in the second example?

• EF is equal to ED

• EF is less than ED

• EF is not comparable to ED

• EF is greater than ED

Which theorem is used to compare sides based on given angles in the second example?

• Side-Side-Side Inequality

• Side-Side-Angle Inequality

• Angle-Side-Angle Inequality

• Side-Angle-Side Inequality

In the final example, which property is used to state that AC is equal to AC?

• Symmetric property

• Transitive property

• Associative property

• Reflexive property

What is the relationship between angle one and angle two in the final proof?

• Angle one is equal to angle two

• Angle one is less than angle two

• Angle one is greater than angle two

• Angle one is not comparable to angle two