Inequality Definitions, Postulates, and Theorems

Question 1

Trichotomy Postulate

Answer 1

Exactly one of the following is true (for real numbers): a > b, a - b, or a < b

Question 2

Transitive Property of Inequality

Answer 2

If a > B and B > c, then a > c

Question 3

Substitution property of inequality

Answer 3

A quantity may be substituted for its equal in any inequality.

Question 4

What are the two addition postulates? (Write them out fully during tests)

Answer 4

1. If equal quantities are added to unequal quantities, then the sums are unequal in the same order.
2. If unequal quantities are added to unequal quantities, then the sums are unequal in the same order

Question 5

What are the two subtraction postulates? (Write them out fully during tests)

Answer 5

1. If equal quantities are subtracted from unequal quantities, then the differences are unequal in the same order.
2. If unequal quantities are subtracted from equal quantities, then the differences are unequal in reverse order

Question 6

Exterior Angle Inequality (Write it out fully during tests)

Answer 6

The measure of an exterior angle is greater than the measure of either remote interior angle.

Question 7

Exterior angle (definition)

Answer 7

An exterior angle of a triangle is an angle that forms a linear pair with an angle of the triangle

Question 8

The triangle inequality theorem (write it out fully during tests)

Answer 8

The sum of the measures of any two sides of a triangle is greater than the measure of the third side

Question 9

The scalene inequality (write it out fully during tests)

Answer 9

If the measures of two angles of a triangle are unequal, then the measures of the sides opposite these angles are unequal in the same order.

Question 10

Parallel lines (definition)

Answer 10

Lines that are coplanar and distinct and do not intersect

Question 11

If two lines are cut by a transversal and they __________________, then they are parallel. (Four phrases fit into the blank)

Answer 11

1. form a pair of congruent alternative interior angles
2. Form a pair of congruent alternate exterior angles
3. Form a pair of congruent corresponding angles
4. Form a pair of same side interior angles that are supplementary

Question 12

If two lines are _________ to the same line, then they are parallel.

Answer 12

Perpendicular

Question 13

Transitive property for parallel lines

Answer 13

If two lines are parallel to the same line, then they are also parallel.

Question 14

If two parallel lines are cut by a transversal, then ___________________. (Four things can go in the blank)

Answer 14

1. Each pair of alternate interior angles is congruent
2. Each pair of alternate exterior angles is congruent
3. Each pair of corresponding angles is congruent
4. Each pair of the same side interior angles is supplementary

Question 15

If two lines are parallel, then a line ______ to one of them is also ______ to the other. (Two things can go in each blank.)

Answer 15

1. parallel, parallel,
2. perpendicular, perpendicular

Question 16

The parallel postulate

Answer 16

Through a given point NOT on the line, there exists exactly one line that is parallel to the given line

Question 17

The measure of an _______ of a triangle is equal to the ____ of the measures of the two _________.

Answer 17

exterior angle, sum, remote interior angles

Question 18

The sum of the ________ of the three ________ of a triangle is ____.

Answer 18

Measures, interior angles, 180 degrees