Chapter 2 - Reasonings and Proofs

Question 1

Postulates about planes

Answer 1

• a plane is defined by three non-collinear points and can be drawn to include any three points
• if two pints lie in a plane, the line containing them lies in the plane
• if two planes intersect, their intersection is a line

Question 2

Addition Property of Equality

Answer 2

If a = b, a + c = b + c

Question 3

Subtraction Property of Equality

Answer 3

If a = b, a - c = b - c

Question 4

Multiplication Property of Equality

Answer 4

If a = b, a(c) = a(c)

Question 5

Division Property of Equality

Answer 5

If a = b, a/c = b/c (if c isn’t equal to 0)

Question 6

Substitution Property of Equality

Answer 6

“a” can be sub substituted for “b” in any equation or expression

Question 7

Distributive Property

Answer 7

a(b+c) = ab + ac

Question 8

Postulates About Lines

Answer 8

• A line is defined by and can be drawn through any two points
• if two angles intersect, their intersection is exactly one point

Question 9

Postulates About Planes

Answer 9

• A plane is defined by three non - collinear points and can be drawn to include any three points
• if two points lie in a plane, the line containing them lies in the plane
• if two planes intersect, their intersection is a line

Question 10

Assumptions

Answer 10

DON’T ASSUME ANYTHING ABOUT THE SIZE OF UNMARKED SIDES AND ANGLES

Question 11

Reflexive Property of Equality

Answer 11

Basically everything equals it’s self (AB = AB)

Question 12

Symmetric Property of Equality

Answer 12

Basically, you can rearrange the same numbers or letters and it will still be equal (AB = BA)

Question 13

Transitive Property of Equality

Answer 13

If AB = CD and CD = EF then AB = EF

Question 14

Properties of Congruence

Answer 14

DIFFERENT FROM PROPERTIES OF EQUALITY (see 2.3 notes)

Question 15

Right Angle Congruence Theorem

Answer 15

All right angles are congruent

Question 16

Vertical Angles Congruence Theorem

Answer 16

All vertical angles are congruent

Question 17

Linear Pair Postulate

Answer 17

Angles in a linear pair are supplements

Question 18

Congruent Complements Theorem

Answer 18

If two angles are complementary to the same angle (or congruent angles), they are congruent to each other

Question 19

Congruent Supplements Theorem

Answer 19

If two angles are supplementary to the same angle (or congruent angles) they are congruent to each other

Question 20

Postulates About Planes

Answer 20

• A plane is defined by three non - collinear points and can be drawn to include any three points
• if two points lie in a plane, the line containing them lies in the plane
• if two planes intersect, their intersection is a line

Question 21

Assumptions

Answer 21

DON’T ASSUME ANYTHING ABOUT THE SIZE OF UNMARKED SIDES AND ANGLES

Question 22

Reflexive Property of Equality

Answer 22

Basically everything equals it’s self (AB = AB)

Question 23

Symmetric Property of Equality

Answer 23

Basically, you can rearrange the same numbers or letters and it will still be equal (AB = BA)

Question 24

Transitive Property of Equality

Answer 24

If AB = CD and CD = EF then AB = EF

Question 25

Properties of Congruence

Answer 25

DIFFERENT FROM PROPERTIES OF EQUALITY (see 2.3 notes)

Question 26

Right Angle Congruence Theorem

Answer 26

All right angles are congruent

Question 27

Vertical Angles Congruence Theorem

Answer 27

All vertical angles are congruent

Question 28

Linear Pair Postulate

Answer 28

Angles in a linear pair are supplements

Question 29

Congruent Complements Theorem

Answer 29

If two angles are complementary to the same angle (or congruent angles), they are congruent to each other

Question 30

Congruent Supplements Theorem

Answer 30

If two angles are supplementary to the same angle (or congruent angles) they are congruent to each other