Triangle Properties and Angle Relationships

The video tutorial covers the exterior angle inequality theorem, explaining that the measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles. It provides examples to illustrate this concept and discusses how to identify angles greater than a given angle. Additionally, the video explains the relationship between the longest and shortest sides of a triangle and their opposite angles.

What does the exterior angle inequality theorem state?

• An exterior angle is equal to one of the remote interior angles.

• An exterior angle is less than either of the remote interior angles.

• An exterior angle is greater than either of the remote interior angles.

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

In a triangle, if angle 4 is an exterior angle, which angles are the remote interior angles?

• Angles 1 and 3

• Angles 1 and 2

• Angles 2 and 3

• Angles 3 and 4

Which angles are less than the measure of angle 4 in the given triangle?

• Angles 2 and 3

• Angles 1 and 3

• Angles 1 and 2

• Angles 3 and 4

If angle 7 is a remote interior angle, which angle is greater than angle 7?

• Angle 5

• Angle 6

• Angle 9

• Angle 8

Which angle is greater than angle 2 in the given triangle?

• Angle 5

• Angle 4

• Angle 3

• Angle 6

In a triangle, the longest side is opposite which angle?

• The smallest angle

• A right angle

• An exterior angle

• The largest angle

If the length of side BC is greater than side AC, which angle is larger?

• Angle A

• Angle B

• Angle C

• Angle D

In triangle DEF, if angle D is 120 degrees and angle E is 30 degrees, which segment is longer?

• Segment FG

• Segment DF

• Segment EF

• Segment DE

In triangle DEF, if segment EF is opposite a 120-degree angle, what can be said about its length?

• It is equal to segment DF.

• It is the shortest side.

• It is the longest side.

• It is shorter than segment DE.

In triangle DEF, if segment DF is opposite a 30-degree angle, what can be said about its length?

• It is the shortest side.

• It is equal to segment EF.

• It is longer than segment DE.

• It is the longest side.