Postulates and Theorems

Question 1

Line Axiom Postulate

Answer 1

Given any two distinct points, exactly one line contains them both

Question 2

The Partition Postulate

Answer 2

A whole is equal to the sum of its parts

Question 3

Reflexive Property of Equality

Answer 3

A quantity is equal to itself

Question 4

Symmetry Property of Equality

Answer 4

Equal quantities may be expressed in any order

Question 5

Transitive Property of Equality

Answer 5

If two quantities are equal to the same quantity, then the two quantities are equal to each other

Question 6

Substitution Property of Equality

Answer 6

A quantity may be substituted for its equal in any expression

Question 7

Addition Property of Equality

Answer 7

If equal quantities are added to equal quantities, then the sums or equal

Question 8

Reflexive Property of Congruence

Answer 8

A segment or angle is congruent to itself

Question 9

Symmetric Property of Congruence

Answer 9

Congruent segments or angles may be expressed in either order

Question 10

Transitive Property of Congruence

Answer 10

If two segments or angles are congruent to the same segment or angle, then the two segments or angles are congruent to each other

Question 11

Substitution Property of Congruence

Answer 11

A segment or angle may be substituted for its congruent in any expression

Question 12

Addition Theorem of Congruence

Answer 12

If congruent segments or angles are added to congruent segments or angles than the resulting segments or angles (sums) are congruent

Question 13

Subtraction Theorem of Congruence

Answer 13

If congruent segments or angles are subtracted from congruent segments or angles then the resulting segments or angles (difference) are congruent

Question 14

Multiplication Property of Equality

Answer 14

If a = b, then ca = cb.

Question 15

Division Property of Equality

Answer 15

If a = b, then a/c = b/c

Question 16

Division Theorem of Congruence

Answer 16

Quotients of congruences are congruent. (Special cases: halves of congruent line segments or halves of congruent angles are congruent.)

Question 17

Multiplication Theorem of Congruence

Answer 17

Multiples of congruences are congruent. (Special cases: doubles of congruent line segments or doubles of congruent angles are congruent.)

Question 18

Theorem for Supplementary Angles (This is not the name of the theorem, you should write out the definition of this during tests)

Answer 18

If two angles are supplementary to the same angle, then they are congruent. If two angles are supplementary to congruent angles, then they are congruent.

Question 19

Theorem for Complementary Angles (This is not the name of the theorem, you should write out the definition of this during tests)

Answer 19

If two angles are supplementary to the same angle, then they are congruent. If two angles are complementary to congruent angles, then they are congruent.

Question 20

Theorem for Vertical Pairs (This is not the name of the theorem, you should write out the definition of this during tests)

Answer 20

If two angles form a vertical pair, then they are congruent.

Question 21

Linear Pair Postulate

Answer 21

If two angles form a linear pair, then they are supplementary.

Question 22

Equidistance Theorems

Answer 22

1. If two points are each equidistant form the endpoints of a life segment, then the line joining them will be the perpendicular bisector of the line segment.
2. If a point is on the perpendicular bisector of a line segment, then it is equidistant from the endpoints of the line segment
3. If a pointt is equidistant from the endpoints of a line segment, then it lies on the perpendicular bisector of the line segment.