Understanding the Exterior Angle Inequality Theorem

The video tutorial explains the exterior angle inequality theorem, which states that the exterior angle of a triangle is greater than any of its remote interior angles. It contrasts this with the exterior angle theorem, which states that the exterior angle is the sum of the remote interior angles. The video includes a diagram to illustrate these concepts and provides an example of a two-column proof to demonstrate the application of the exterior angle inequality theorem. The tutorial concludes with a discussion on how to use this theorem in geometric proofs.

What is the main idea of the Exterior Angle Inequality Theorem?

• The exterior angle is equal to the sum of the interior angles.

• The exterior angle is less than any one of the remote interior angles.

• The exterior angle is greater than any one of the remote interior angles.

• The exterior angle is equal to the remote interior angles.

In the example provided, which angle is identified as the exterior angle?

• Angle 1

• Angle 2

• Angle 3

• Angle 4

What is the relationship between angle four and angles one and two according to the Exterior Angle Inequality Theorem?

• Angle four is equal to angle one and two.

• Angle four is less than angle one or two.

• Angle four is less than angle one and two.

• Angle four is greater than angle one or two.

How does the Exterior Angle Theorem differ from the Exterior Angle Inequality Theorem?

• It states that the exterior angle is greater than the sum of the remote interior angles.

• It states that the exterior angle is equal to the sum of the remote interior angles.

• It states that the exterior angle is equal to one of the remote interior angles.

• It states that the exterior angle is less than the sum of the remote interior angles.

Which theorem states that the exterior angle is the sum of the remote interior angles?

• Remote Interior Angle Theorem

• Exterior Angle Theorem

• Interior Angle Theorem

• Exterior Angle Inequality Theorem

What is the first step in applying the Exterior Angle Inequality Theorem in a two-column proof?

• Identify the remote interior angles.

• Prove that the exterior angle is equal to the sum of the interior angles.

• State that the exterior angle is greater than one of the remote interior angles.

• Draw a diagram of the triangle.

In the proof, which angle is shown to be greater than angle three?

• Angle 5

• Angle 4

• Angle 2

• Angle 1

What property of inequalities is used to conclude the proof?

• If one angle is equal to another, they are congruent.

• If one angle is greater than a second, and the second is greater than a third, then the first is greater than the third.

• If one angle is less than another, they are supplementary.

• If one angle is greater than another, they are complementary.

In the proof, which angle is identified as the remote interior angle when angle two is the exterior angle?

• Angle 1

• Angle 3

• Angle 4

• Angle 5

What is the purpose of drawing a different picture in the proof?

• To show that angle two is less than angle three.

• To illustrate that angle two is the exterior angle and angle three is the remote interior angle.

• To prove that angle one is equal to angle three.

• To demonstrate that angle three is greater than angle two.