CONJECTURE (PAGE 4)

AN UNPROVEN STATEMENT THAT IS BASED UPON OBSERVATION.

INDUCTIVE REASONING (PAGE 4)

PROCESS OF LOOKING FOR PATTERNS AND MAKING CONJECTURES (AN UNPROVEN STATEMENT THAT IS BASED UPON OBSERVATION)

COUNTEREXAMPLE (PAGE 4)

AN EXAMPLE THAT SHOWS A CONJECTURE IS FALSE.

DEFINITION, UNDEFINED

(PAGE 10)

A DEFINITION USES KNOWN WORDS TO DESRIBE A NEW WORD.  IN GEOMETRY SOME WORDS, SUCH AS POINT, LINE AND PLANE ARE UNDEFINED TERMS.

POINT (PAGE 10)

HAS NO DIMENSION.  REPRESENTED BY A SMALL DOT.

LINE (PAGE 10)

EXTENDS IN ONE DIMENSION.  REPRESENTED BY A STRAIGHT LINE WITH TWO ARROWHEADS TO INDICATE THAT THE LINE EXTENDS WITHOUT END IN 2 DIRECTIONS.

PLANE (PAGE 10)

EXTENDS IN TWO DIMENSIONS.  REPRESENTED BY A SHAPE THAT LOOKS LIKE A TABLETOP OR A WALL.  NEED TO IMAGINE IT EXTENDS WITHOUT END, ALTHOUGH IT WILL APPEAR TO HAVE EDGES.

COLLINEAR POINTS (PAGE 10)

POINTS THAT LIE ON THE SAME LINE

COPLANAR POINTS (PAGE 10)

POINTS THAT LIE ON THE SAME PLANE

LINE SEGMENT (PAGE 11)

SYMBOLIZED BY AB; CONSISTS OF THE ENDPOINTS A & B AND ALL POINTS THAT ARE BETWEEN A & B

ENDPOINTS (PAGE 11)

THE TWO POINTS DEFINING A LINE SEGMENT OR SEGMENT

RAY (PAGE 11)

PART OF A LINE; HAS ONE ENDPOINT AND THE OTHER END KEEPS GOING.

OPPOSITE RAYS (PAGE 11)

Two rays with a common endpoint that form a line.

POSTULATE

A STATEMENT ASSUMED TO BE TRUE WITHOUT PROOF. 

AXIOMS (PAGE 17)

ANY MATHEMATICAL STATEMENT WHICH SERVES AS A STARTING POINT FROM WHICH OTHER STATEMENTS ARE LOGICALLY DERIVED.

COORDINATE (PAGE 17)

A NUMBER THAT IDENTIFIES A POINT ON A NUMBER LINE, ON A PLANE OR IN SPACE.

DISTANCE (PAGE 17)

THE DISTANCE BETWEEN POINTS A & B IS WRITTEN AS AB

DISTANCE FORMULA (PAGE 19)

GIVEN THE TWO POINTS (x₁, y₁) & (x₂, y₂), THE DISTANCE BETWEEN THESE POINTS IS GIVEN BY THE FORMULA:

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CONGRUENT SEGMENTS (PAGE 19)

TWO LINE SEGMENTS THAT ARE THE SAME.

ANGLE (PAGE 26)

THE UNION OF 2 RAYS THAT HAVE THE SAME ENDPOINT; MEASURED IN DEGREES; THE FIVE TYPES OF ANGLES ARE ZERO, ACUTE, RIGHT, OBTUSE & STRAIGHT.

CONGRUENT ANGLES (PAGE 26)

SAME ANGLE IN DEGREES.

THEY DON'T HAVE TO POINT IN THE SAME DIRECTION.

THEY DON'T HAVE TO BE SIMILAR SIZED LINES.

ACUTE ANGLE (PAGE 28)

AN ANGLE THAT IS LESS THAN 90 DEGREES.

OBTUSE ANGLE (PAGE 28)

AN ANGLE THAT IS GREATER THAN 90 DEGREES, BUT LESS THAN 180 DEGREES.

RIGHT ANGLE (PAGE 28)

AN ANGLE THAT IS EXACTLY 90 DEGREES.

STRAIGHT ANGLES (PAGE 28)

AN ANGLE THAT IS EXACTLY 180 DEGREES.

ADJACENT ANGLE (PAGE 28)

ANGLES THAT SHARE A COMMON VERTEX AND SIDE, BUT HAVE NO COMMON INTERIOR POINTS.

INITIAL POINT (PAGE 11)

THE BEGINNING END OF THE RAY AB

INTERSECT (PAGE 12)

TWO OR MORE GEOMETRIC FIGURES THAT HAVE ONE OR MORE POINTS IN COMMON.

INTERSECTION (PAGE 12)

THE SET OF POINTS TWO OR MORE INTERSECTING FIGURES HAVE IN COMMON.

DISTANCE (PAGE 17)

THE ABSOLUTE VALUE OF THE DIFFERENCE BETWEEN TWO COORDINATES.

THEOREM (PAGE 17)

RULES THAT ARE PROVEN.

MIDPOINT (PAGE 34)

THE POINT THAT DIVIDES A SEGMENT INTO TWO CONGRUENT SEGMENTS.

BISECT (PAGE 34)

SAME AS MIDPOINT-THE POINT THAT DIVDES A SEGMENT INTO TOW CONGRUENT SEGMENTS.

SEGMENT BISECTOR (PAGE 34)

A SEGMENT, RAY, LINE OR PLANE THAT INTERSECTS A SEGMENT AT ITS MIDPOINT.

COMPASS (PAGE 34)

A DRAWING TOOL USED TO DRAW CIRCLES.

STRAIGHTEDGE (PAGE 34)

RULER WITHOUT MARKS

CONSTRUCT, CONSTRUCTION (PAGE 34)

A PRECISE WAY OF DRAWING WHICH ALLOWS ONLY THE USE OF A COMPASS AND A STRAIGHTEDGE.

MIDPOINT FORMULA (PAGE 35)

FORMULA TO CALCULATE THE MIDPOINT OF A SEGMENT; NEED TO KNOW THE ENDPOINTS.  TAKE THE AVERAGE OF THE X & Y COORDINATES

If A(x₁y) and B(x₂y₂) then (x₁+x_2, y₁+y₂)

ANGLE BISECTOR (PAGE 36)

A RAY THAT DIVIDES AN ANGLE INTO TWO ADJACENT ANGLES THAT ARE CONGRUENT.

VERTICAL ANGLES (PAGE 44)

TWO ANGLES WHOSE SIDES FORM TWO PAIRS OF OPPOSITE RAYS.

LINEAR PAIR (PAGE 44)

TWO ADJACENT ANGLES WHOSE NONCOMMON SIDES ARE OPPOSITE RAYS.

COMPLEMENTARY ANGLES (PAGE 46)

TWO ANGLES WHOSE SUM OF THEIR MEASURE IS 90 DEGREES.

COMPLEMENT OF AN ANGLE (PAGE 46)

THE TWO ANGLES FORMED BY A COMPLEMENTARY ANGLE.  THEY CAN BE ADJACENT OR NONADJACENT.

SUPPLEMENTARY ANGLES (PAGE 46)

TWO ANGLES WHOSE SUME OF THEIR MEASURE IS 180 DEGREES.

SUPPLEMENT OF AN ANGLE (PAGE 46)

THE TWO ANGLES OF A SUPPLEMENTARY ANGLE.  THEY CAN BE ADJACENT OR NONADJACENT.

CONDITIONAL STATEMENT (PAGE 71)

A TYPE OF LOGICAL STATEMENT, CONTAINS TWO PARTS-HYPOTHESIS AND CONCLUSION. 

CAN BE EITHER TRUE OR FALSE.  FOR IT TO BE TRUE, ARGUMENT MUST PROVE THAT ALL CASES FULFILL THE HYPOTHESIS.

IF-THEN FORM (PAGE 71)

THE TWO PARTS OF A CONDITIONAL STATEMENT.  THE IF REPRESENTS THE HYPOTHESIS; THE THEN REPRESENTS THE CONCLUSION.

HYPOTHESIS (PAGE 71)

THE PART OF THE CONDITIONAL STATEMENT THAT MUST BE PROVEN.  THE FIRST PART, USUALLY.

CONCLUSION (PAGE 71)

THE PART OF THE IF-THEN STATEMENT THAT REPRESENTS THE 'THEN' PORTION OF THE CONDITIONAL STATEMENT.

CONVERSE (PAGE 72)

A CONDITIONAL STATEMENT FORMED BY SWITCHING THE HYPOTHESIS AND THE CONCLUSION.

If you see lightning, then you hear thunder.-Conditional Statement

If you hear thunder, then you see lightning.-Converse

NEGATION (PAGE 72)

WRITING THE NEGATIVE OF A CONDITIONAL STATEMENT.

m Angle A = 30 degrees; Angle A is Acute-Conditional Statement

m Angle A = 30 degrees; Angle A is not acute-Negation

INVERSE (PAGE 72)

NEGATING THE HYPOTHESIS AND CONCLUSION OF THE CONDITIONAL STATEMENT.

CONTRAPOSITIVE (PAGE 72)

WHEN YOU NEGATE THE HYPOTHESIS AND CONCLUSION OF THE CONVERSE OF A CONDITIONAL STATEMENT.

EQUILAVENT STATEMENT (PAGE 72)

TWO STATEMENTS THAT ARE BOTH TRUE OR BOTH FALSE.  A CONDITIONAL STATEMENT IS EQUIVALENT TO ITS CONTRAPOSITIVE. THE INVERSE AND CONVERSE OF A CONDITIONAL STATEMENT ARE EQUIVALENT .

PERPENDICULAR LINES (PAGE 79)

TWO LINES THAT INTERSECT TO FORM A RIGHT ANGLE.

LINE PERPENDICULAR TO A PLANE (PAGE 79)

A LINE THAT INESECTS THE PLANE IN A POINT AN IS PERPENDICULAR TO EVERY LINE IN THE PLANE THAT INTERSECTS IT. 

BICONDITIONAL STATEMENT (PAGE 80)

A STATEMENT CONTAINING THE PHRASE "IF AND ONLY IF".  EQUAL TO WRIGINT A CONDITIONAL STATEMENT AND ITS CONVERSE.

LOGICAL ARGUMENT (PAGE 89)

A FORM OF DEDUCTIVE REASONING WHICH USES FACTS, DEFINITIONS AND ACCEPTED PROPERTIES IN A LOGICAL ORDER.

LAW OF DETACHMENT (PAGE 89)

ONE OF TWO LAWS OF DEDUCTIVE REASONING.

IF P     Q IS A TRUE CONDITIONAL STATEMENT AND P IS TRUE, THE Q IS TRUE.

LAW OF SYLLOGISM (PAGE 90)

THE SECOND LAW OF DEDUCTIVE REASONING

IF P   Q AND Q   R ARE TRUE CONDITIONAL STATEMENTS, THEN P   R IS TRUE.

THEOREM (PAGE 102)

A TRUE STATEMENT THAT FOLLOWS AS A REULT OF OTHER TRUE STATEMENTS.

TWO-COLUMN PROOF (PAGE 102)

CONTAINS NUMBERED STATEMENTS AND REASONS THAT SHOW THE LOGICAL ORDER OF AN ARGUMENT.