Geometry-Chapter 2-Reasoning And Proof

Front 1

Conjecture

Back 1

Unproven statement based on observations.

Front 2

Inductive Reasoning

Back 2

Finding a pattern in specific cases and then expanding it to general cases.

Hint 2

Specific → General

Front 3

Deductive Reasoning

Back 3

Finding a pattern in general cases and then expanding it to specific cases.

Hint 3

General → Specific

Front 4

Counterexample

Back 4

Specific case in which the conjecture is false.

Front 5

Right Angles Congruence Theorem

Back 5

All right angles are congruent.

Front 6

Congruent Supplements Theorem

Back 6

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

Front 7

Law of Syllogism

Back 7

Transitive property; "If P then Q. If Q then R. Thus, if P, then R.

Front 8

Congruent Complements Theorem

Back 8

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

Front 9

Linear Pair Postulate

Back 9

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

Front 10

Vertical Angles Congruence Theorem

Back 10

Vertical angles are congruent.

Front 11

Conditional Statement

Back 11

Logical statement that has two parts: a hypothesis and a conclusion. Written in if-then form.

Front 12

Negation

Back 12

Opposite of the original statement.

Front 13

Converse

Back 13

A conditional statement with the hypothesis and conclusion exchanged. •If y, then x.•

Front 14

Inverse

Back 14

A conditional statement with both the hypothesis and conclusion negated. •If not x, then not y.•

Front 15

Contrapositive

Back 15

A negation of the converse of a conditional statement. •If not y, then not x.•

Front 16

Equivalent Statements

Back 16

Two statements that are either both true or both false.

Front 17

Perpendicular Lines

Back 17

If two lines intersect to form a right angle, then they are perpendicular.

Front 18

Postulate 5

Back 18

Through any two points there exists exactly one line.

Front 19

Postulate 6

Back 19

A line contains at least two points.

Front 20

Postulate 7

Back 20

If two lines intersect, then their intersection is exactly one point.

Front 21

Postulate 8

Back 21

Through any three noncollinear points there exists exactly one plane.

Front 22

Postulate 9

Back 22

A plane contains at least three noncollinear points.

Front 23

Postulate 10

Back 23

If two points lie in a plane, then the line containing them lies in the plane.

Front 24

Postulate 11

Back 24

If two planes intersect, then their intersection is a line.

Front 25

Line perpendicular to a plane

Back 25

Line intersects the plane in a point and is perpendicular to every line in the plane that intersects it at that point.

Front 26

Addition Property

Back 26

If a=b, then a+c=b+c.

Front 27

Subtraction Property

Back 27

If a=b, then a-c=b-c.

Front 28

Multiplication Property

Back 28

If a=b, then ac=bc.

Front 29

Division Property

Back 29

If a=b and c does not equal zero, then a/c=b/c.

Front 30

Substitution Property

Back 30

If a=b, then a can be substituted for b in any equation or expression.

Front 31

Distributive Property

Back 31

a(b+c)=ab+ac, where a, b, and c are real numbers.

Front 32

Reflexive Property of Equality

Back 32

Real Numbers- For any real number a, a=a. Segment Length- For any segment AB, AB=AB. Angle Measure- For any angle A, the measure of Angle A equals the measure of Angle A.

Front 33

Symmetric Property of Equality

Back 33

Real Numbers- For any real numbers a and b, if a=b, then b=a. Segment Length- For any segments AB and CD, if AB=CD, then CD=AB. Angle Measure- For any angles A and B, if the measure of Angle A equals the measure of Angle B, then the measure of Angle B equals the measure of Angle A.

Front 34

Transitive Property of Equality

Back 34

Real Numbers- For any real numbers a, b, and c, if a=b and b=c, then a=c. Segment Length- For any segments AB, CD, and EF, if AB=CD and CD=EF, then AB=EF. Angle Measure- For any angles A, B, and C, if the measure of Angle A equals the meausre of Angle B and the measure of Angle B equals the measure of Angle C, then the measure of Angle A equals the measure of Angle C.

Front 35

Proof

Back 35

A logical argument that shows a statement is true.

Front 36

Two-Column Proof

Back 36

Has numbered statements and corresponding reasons that show an argument in a logical order.

Front 37

Theorem

Back 37

A statement that can be proven.

Front 38

Congruence of Segments

Back 38

Reflexive- For any segment AB, AB is congruent to AB. Symmetric- If AB is congruent to CD, then CD is congruent to AB. Transitive- If AB is congruent to CD and CD is congruent to EF, then AB is congruent to EF.

Front 39

Congruence of Angles

Back 39

Reflexive- For any angle A, the measure of Angle A is congruent to the measure of Angle A. Symmetric- If the measure of Angle A is congruent to the measure of Angle B, then the measure of Angle B is congruent to the measure of Angle A. Transitive- If the measure of Angle A is congruent to the measure of Angle B and the measure of Angle B is congruent to the measure of Angle C, then the measure of Angle A is congruent to the measure of Angle C.

Front 40

Congruent Supplements Theorem

Back 40

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

Front 41

Congruent Complements Theorem

Back 41

If two angles are complementary to the same angle (or to congruent angles), then they are congruent.