Understanding Inequalities in Triangles

What is the definition of an inequality between two real numbers a and b?

• a is equal to b

• a is greater than b if a = b - c

• a is greater than b if there exists a number c such that a = b + c

• a is less than b

Which property allows us to conclude that if a < b and b < c, then a < c?

• Addition property

• Subtraction property

• Transitive property

• Symmetric property

According to the exterior angle theorem, the measure of an exterior angle is equal to:

• The measure of the adjacent interior angle

• The sum of all interior angles

• The difference between the two adjacent interior angles

• The sum of the two non-adjacent interior angles

If angle 14 is an exterior angle, which of the following is true?

• Angle 14 is equal to angle 4

• Angle 14 is greater than angle 4 and angle 11

• Angle 14 is less than angle 4

• Angle 14 is less than angle 11

What is the relationship between angle 11 and angles 6 and 7 if angle 11 is an exterior angle?

• Angle 11 is equal to angles 6 and 7

• Angle 11 is less than angles 6 and 7

• Angle 11 is greater than angles 6 and 7

• Angle 11 is unrelated to angles 6 and 7

In a triangle, if one side is longer than another, what can be said about the angles?

• The angles are equal

• The angle opposite the longer side is larger

• The angle opposite the longer side is smaller

• The angle opposite the longer side is unrelated

If angle J is greater than angle K, what can be inferred about the sides opposite these angles?

• Sides opposite both angles are unrelated

• Sides opposite both angles are equal

• Side opposite angle J is longer than side opposite angle K

• Side opposite angle J is shorter than side opposite angle K

Which side is opposite the smallest angle in triangle ABC?

• Side BC

• Side AC

• Side CA

• Side AB

In triangle ABC, if side AB is the smallest, which angle is the smallest?

• Angle A

• Angle B

• Angle C

• Angle D

When listing sides from shortest to longest, which side comes first if angle A is the smallest?

• Side BC

• Side AB

• Side CA

• Side AC