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Definitions

Complementary Angles

Supplementary angles

theorem

Definitions

Two angles whose measures equal 90 degrees

two angles whose measures equal 180 degrees

a statement that can be proven

Definitions

Definitions

Complementary Angles

Two angles whose measures equal 90 degrees

Through any two points there

If two distinct lines intersect,

If two distinct planes intersect,

Through any three non-collinear points,

is exactly one line.

they intersect in exactly one point.

they intersect in exactly one line.

there is exactly one plane.

Through any two points there

is exactly one line.

If two distinct lines intersect,

they intersect in exactly one point.

Complementary Angles

Supplementary angles

theorem

Vertical angles

Two angles whose measures equal 90 degrees

two angles whose measures equal 180 degrees

a statement that can be proven

4 angles formed by intersecting lines and facing in four diff…

Complementary Angles

Two angles whose measures equal 90 degrees

Supplementary angles

two angles whose measures equal 180 degrees

Segment Addition Postulate

Protractor Postulate

Parallel Lines

Skew Lines

AB + BC = AC

Says that you can measure any angle

two lines that don't intersect and are coplanar

two lines that don't intersect and aren't coplanar

Segment Addition Postulate

AB + BC = AC

Protractor Postulate

Says that you can measure any angle

they are congruent.... Right Angles Cong…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Complem…

If two angles are right angles, then

If two angles are supplementary to the same angle, then

If two angles are supplementary to congruent angles, then

If two angles are complementary to the same angle, then

they are congruent.... Right Angles Cong…

If two angles are right angles, then

they are congruent.... Congruent Supplem…

If two angles are supplementary to the same angle, then

they are congruent.... Right Angles Cong…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Complem…

If two angles are right angles, then

If two angles are supplementary to the same angle, then

If two angles are supplementary to congruent angles, then

If two angles are complementary to the same angle, then

they are congruent.... Right Angles Cong…

If two angles are right angles, then

they are congruent.... Congruent Supplem…

If two angles are supplementary to the same angle, then

Definition

Postulate

Theorem

Line Segment

a list of properties an object must have

a basic assumption

a statement that has been proven true

two points on a line and all points that lie between them

Definition

a list of properties an object must have

Postulate

a basic assumption

Area Formula for a Triangle in terms o…

Law of Sines

Law of Cos

Arc Addition Postulate

area= 1/2 x side1 x side2 x sin(included angle)

Sin(A)/a=Sin(B)/b=Sin(C)/c

a^2=b^2+c^2-2(bc)Cos(A)... b^2=a^2+c^2-2(ac)Cos(B)... c^2=a^2+b^2-2…

The measure of an arc formed by 2 adjacent arcs is the sum of…

Area Formula for a Triangle in terms o…

area= 1/2 x side1 x side2 x sin(included angle)

Law of Sines

Sin(A)/a=Sin(B)/b=Sin(C)/c

Line tangent to circle→Line perpendicu…

Line perpendicular to radius→line tang…

2 segments tangent to circle from same…

Arc addition postulate

If a line is tangent to a circle, then the line is perpendicu…

If a line is perpendicular to the radius, then it is tangent…

If two segments are tangent to a circle from the same externa…

the measure of an arc formed by two adjacent arcs is the sum…

Line tangent to circle→Line perpendicu…

If a line is tangent to a circle, then the line is perpendicu…

Line perpendicular to radius→line tang…

If a line is perpendicular to the radius, then it is tangent…

Law Of Detachment

Law Of Syllogism

Linear Pair Theorem

Congruent Supplements Theorem

If P>Q is a true statement and P is true, then Q is true

If P>Q and Q>R are true statements, then P>R is a true statem…

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

If two angles are supplementary to the same angle, then the t…

Law Of Detachment

If P>Q is a true statement and P is true, then Q is true

Law Of Syllogism

If P>Q and Q>R are true statements, then P>R is a true statem…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be matched one to one with the real…

If B is between A and C ... then AB + BC = AC.... If AB + BC = AC,…

Consider ray OB and a point A on one side of ray OB .... The ray…

Words If P is in the interior of ∠ RST, then the measure of ∠…

Ruler Postulate

The points on a line can be matched one to one with the real…

Segment Addition Postulate

If B is between A and C ... then AB + BC = AC.... If AB + BC = AC,…

Postulate 1-1-1

Postulate 1-1-2

Postulate 1-1-3

Postulate 1-1-4

Through any two points there is exactly one line

Through any three noncollinear points there is exactly one pl…

If two points lie in a plane, then the line containing those…

If two lines intersect, then they intersect in exactly one po…

Postulate 1-1-1

Through any two points there is exactly one line

Postulate 1-1-2

Through any three noncollinear points there is exactly one pl…

Isosceles Triangle Theorem

Converse to Isosceles Triangle Theorem

SSS postulate

SAS postulate

If two sides of a triangle are congruent, then the angles opp…

If two angles of a triangle are congruent, then the sides opp…

If three sides of one triangle are congruent to three sides o…

If two sides and the included angle of one triangle are congr…

Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opp…

Converse to Isosceles Triangle Theorem

If two angles of a triangle are congruent, then the sides opp…

Corollaries

Corollaries

Corollaries

Supplementary Angle Theorem

If two angles of one triangle are congruent to two angles of…

Each angle of an equiangular triangle measures sixty degrees

In a triangle there can be at most one right angle or one obt…

All angles which are supplementy to the same or equal angles…

Corollaries

If two angles of one triangle are congruent to two angles of…

Corollaries

Each angle of an equiangular triangle measures sixty degrees

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be matched one to one with real numb…

If B is between A and C, then AB+BC=AC

Consider OB and a point A on one side of OB. The rays of the…

If P is the interior of angleRST, then the measure of angleRS…

Ruler Postulate

The points on a line can be matched one to one with real numb…

Segment Addition Postulate

If B is between A and C, then AB+BC=AC

segment addition postulate (1.2)

midpoint (1.3)

segment bisector (1.3)

angle addition postulate (1.5)

when 3 points are collinear, you can say that one point is be…

midpoint of a segment is the point that divides the segment i…

point, ray line, line segment or plane that intersects the se…

if angle AB is equal to angle BC, then angle AB + angle BC = AC

segment addition postulate (1.2)

when 3 points are collinear, you can say that one point is be…

midpoint (1.3)

midpoint of a segment is the point that divides the segment i…

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

Through any two points, there is exactly one line.

Through any three noncollinear points, there is exactly one p…

A line contains at least two points.

A plane contains at least three noncollinear points.

Postulate 2.1

Through any two points, there is exactly one line.

Postulate 2.2

Through any three noncollinear points, there is exactly one p…

Addition property

subtraction property

multiplication property

division property

if a=b, then a+c=b+c

if a=b, then a-c=b-c

if a=b, then a**c=b**c

if a=b and c does not equal 0, then a/c = b/c

Addition property

if a=b, then a+c=b+c

subtraction property

if a=b, then a-c=b-c

there is exactly one line.

there is exactly one plane.

two points.

three noncollinear points.

Through any two points,

Through any three noncollinear points,

A line contains at least

A plane contains at least

there is exactly one line.

Through any two points,

there is exactly one plane.

Through any three noncollinear points,

undefined term

point

line

plane

a word without a formal definition

undefined, a location with no size or dimension

undefined, a series of infinite points that extends in two di…

undefined, flat surface that has no thickness and extends in…

undefined term

a word without a formal definition

point

undefined, a location with no size or dimension

Ruler postulate

Segment addition postulate

Protractor postulate

Angle addition postulate

the distance between A and B is the Absolute value of the dif…

If B is between A and C, then AB+BC=AC

The measure of angle ABC is equal to the absolute value of th…

If D is in the interior if angle ABC...... m<ABC=m<ABD+m<DBC

Ruler postulate

the distance between A and B is the Absolute value of the dif…

Segment addition postulate

If B is between A and C, then AB+BC=AC

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be matched one to one with the real…

If B is between A and C, then AB+BC=AC.

The measure of ∠AOB, which can be written as m∠AOB, is equal…

If P is in the interior of ∠RST, then the measure of ∠RST is…

Ruler Postulate

The points on a line can be matched one to one with the real…

Segment Addition Postulate

If B is between A and C, then AB+BC=AC.

Segment Addition Postulate

Angle Addition Postulate

Two-Point Postulate

Line-Point Postulate

If B is between A and C, then AB+BC=AC.

If P is in the interior of ∠RST, then the measure of ∠RST is…

Through any two points, there is exactly one line.

A line contains at least two points.

Segment Addition Postulate

If B is between A and C, then AB+BC=AC.

Angle Addition Postulate

If P is in the interior of ∠RST, then the measure of ∠RST is…

Segment Addition Postulate

Angle Addition Postulate

Linear Pair Theorem

Right Angle Congruence Theorem (or Rig…

If B is between A and C, the AB + BC = AC.

If O is in the interior of <ABC, then m<ABO + m<OBC = m<ABC

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

All right angles are congruent.

Segment Addition Postulate

If B is between A and C, the AB + BC = AC.

Angle Addition Postulate

If O is in the interior of <ABC, then m<ABO + m<OBC = m<ABC

angle addition postulate

segment addition postulate

linear pair postulate

corresponding angles postulate

if a point S lies in the interior of ∠PQR, then ∠PQS + ∠SQR =…

if point B is between points A and C, then AB + BC = AC

if two angles form a linear pair, then they are supplementary

if two parallel lines are cut by a transversal, then the pair…

angle addition postulate

if a point S lies in the interior of ∠PQR, then ∠PQS + ∠SQR =…

segment addition postulate

if point B is between points A and C, then AB + BC = AC

Side-Side-Side (SSS) Congruence

Side-Angle-Side (SAS) Congruence

Angle-Side-Angle (ASA) Congruence

Angle-Angle-Side (AAS) Congruence

If three sides of one triangle are congruent to three sides o…

If two sides and the included angle of one triangle are congr…

If two angles and the included side of one triangle are congr…

If two angles and the non-included side of one triangle are c…

Side-Side-Side (SSS) Congruence

If three sides of one triangle are congruent to three sides o…

Side-Angle-Side (SAS) Congruence

If two sides and the included angle of one triangle are congr…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

1. The points on a line can be paired with the real numbers i…

If B is between A and C, then... AB + BC = AC

On ray AB in a given plane, choose any point O between A and…

If point B lies in the interior of <AOC, then... m< AOB + m<BOC…

Ruler Postulate

1. The points on a line can be paired with the real numbers i…

Segment Addition Postulate

If B is between A and C, then... AB + BC = AC

Surface Area

Lateral Area right prism

Volume of right prism

Lateral Area of regular pyramid

lateral area + 2B

Ph (Perimeter x height)

Bh (total area of Base x height)

1/2 P ℓ (ℓ = slant height)

Surface Area

lateral area + 2B

Lateral Area right prism

Ph (Perimeter x height)

Corresponding Angles Postulate

Alternate Interior Angles Theorem

Alternate Exterior Angles Theorem

Same-Side Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pair…

If two parallel lines are cut by a transversal, then the pair…

If two parallel lines are cut by a transversal, then the two…

If two parallel lines are cut by a transversal, then the two…

Corresponding Angles Postulate

If two parallel lines are cut by a transversal, then the pair…

Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pair…

Theorem 2-1: Vertical Angles Theorem

Theorem 2-2: Congruent Supplements The…

Theorem 2-3: Congruent Complements The…

Theorem 2-4

Vertical angles are always congruent.

If 2 angles are supplements of the same angle (or of congruen…

If 2 angles are complements of the same angle (or of congruen…

All right angles are congruent

Theorem 2-1: Vertical Angles Theorem

Vertical angles are always congruent.

Theorem 2-2: Congruent Supplements The…

If 2 angles are supplements of the same angle (or of congruen…

Corresponding Angles

Corresponding Angles Converse

Alternate Interior Angles

Alternate Exterior Angles

If two parallel lines are cut by a transversal, then the pair…

If two lines are cut by a transversal and the corresponding a…

If two parallel lines are cut by a transversal, then the alte…

If two parallel lines are cut by a transversal, then the alte…

Corresponding Angles

If two parallel lines are cut by a transversal, then the pair…

Corresponding Angles Converse

If two lines are cut by a transversal and the corresponding a…

Postulate 1 (Ruler Postulate)

Postulate 2 (Segment Addition Postulate)

Postulate 3 (Protractor Postulate)

Postulate 4 (Angle Addition Postulate)

The distance between points a and b is the absolute value of…

If B is in between A and C, then AB+BC=AC

The measure of angle AOB is equal to the absolute value of th…

If point B is in the interior of angle COA, then the measure…

Postulate 1 (Ruler Postulate)

The distance between points a and b is the absolute value of…

Postulate 2 (Segment Addition Postulate)

If B is in between A and C, then AB+BC=AC

Postulate 1: Ruler Postulate

Postulate 2: Segment Addition Postulate

Postulate 4: The Angle Addition Postul…

Postulate 5

The points on a line can be paired in a one-to-one correspond…

If B is between A and C, then AB + BC = AC

If point D is in the interior of angle ABC, then the m of ang…

Through any two points there is exactly one line.

Postulate 1: Ruler Postulate

The points on a line can be paired in a one-to-one correspond…

Postulate 2: Segment Addition Postulate

If B is between A and C, then AB + BC = AC

Addition property of inequality (≠)

multiplication and division property o…

transitive property of inequality (≠)

Property of inequality (≠)

If a > b and c > d, then a + c > b + d

If a > b and c > 0, then ac > bc and a/c > b/c;... If a > b and…

If a > b and b > c, then a > c

If a = b + c and c > 0, then a > b and a> c

Addition property of inequality (≠)

If a > b and c > d, then a + c > b + d

multiplication and division property o…

If a > b and c > 0, then ac > bc and a/c > b/c;... If a > b and…

Parallelograms- About Sides

Parallelograms- About Angles

Parallelograms- About Diagonals

Parallelogram Converses- About Sides

If a quadrilateral is a parallelogram, the opposite... sides ar…

* If a quadrilateral is a parallelogram, the opposite... angles…

* If a quadrilateral is a parallelogram, the diagonals... bisec…

* If both pairs of opposite sides of a quadrilateral... are par…

Parallelograms- About Sides

If a quadrilateral is a parallelogram, the opposite... sides ar…

Parallelograms- About Angles

* If a quadrilateral is a parallelogram, the opposite... angles…

segment addition postulate (SAP)

angle addition postulate (AAP)

addition property of equality

subtraction property of equality

if B is between A and C, then AB + BC = AC... if AB + BC = AC, t…

Angles can be added together if they are adjacent

Adding a value to each side of an equation... if a=b, then a+c=b+c

subtracting a value from each side of an equation ... if a=b the…

segment addition postulate (SAP)

if B is between A and C, then AB + BC = AC... if AB + BC = AC, t…

angle addition postulate (AAP)

Angles can be added together if they are adjacent

segment addition postulate

angle addition postulate

linear pair postualte

reflexive property

if 3 points a, b, and c are colinear and b is between a and c…

if point b is interior of <aoc; then m<aob + m<boc = m<aoc

if two angles form a linear pair; they must be supplementary

a = a

segment addition postulate

if 3 points a, b, and c are colinear and b is between a and c…

angle addition postulate

if point b is interior of <aoc; then m<aob + m<boc = m<aoc

Corresponding Angles Postulate

Alternate Interior Angles Theorem

Consecutive Interior Angles Theorem

Alternate Exterior Angles Theorem

When 2 lines are cut by a transversal, if the lines are paral…

When 2 lines are but by a transversal, if the lines are paral…

When 2 lines are cut by a transversal, if the lines are paral…

When 2 lines are cut by a transversal, if the lines are paral…

Corresponding Angles Postulate

When 2 lines are cut by a transversal, if the lines are paral…

Alternate Interior Angles Theorem

When 2 lines are but by a transversal, if the lines are paral…

Postulate 1-1-1

Postulate 1-1-2

Postulate 1-1-3

Postulate 1-1-4

Through any two points there is exactly one line.

Through any non collinear points there is exactly one plane c…

If two points lie in a plane, then the line containing these…

If two lines intersect, then they intersect in exactly one pl…

Postulate 1-1-1

Through any two points there is exactly one line.

Postulate 1-1-2

Through any non collinear points there is exactly one plane c…

Law of Detatchment

Law of Syllogism

Ruler Postulate

Segment Addition Postulate

if a conditional is true, and the hypothesis statement is tru…

conclusion that the first statement must be equal to the hypo…

every segment is measureable

pieces add together; parts add to a whole.

Law of Detatchment

if a conditional is true, and the hypothesis statement is tru…

Law of Syllogism

conclusion that the first statement must be equal to the hypo…

Postulate 1

Postulate 2

Postulate 3

Postulate 4

The points on a line can be paired with real numbers in such…

If B is between A and C then AB+BC= AC

When angles can be paired to numbers

When a new angle is added because of a new point

Postulate 1

The points on a line can be paired with real numbers in such…

Postulate 2

If B is between A and C then AB+BC= AC

Postulate #1

Postulate #2

Postulate #3

Postulate #4

through any two points there is exactly one line

through any three noncollinear points there is exactly one pl…

if two points lie in a plane, then the line containing those…

if two lines intersect, then they intersect inn exactly one p…

Postulate #1

through any two points there is exactly one line

Postulate #2

through any three noncollinear points there is exactly one pl…

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

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

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

if a=b, then ac=bc

If a=b and c≠0 then a/c = b/c.

Addition Property of Equality

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

Subtraction Property of Equality

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

exterior angle inequality theorem

statement

converse

inverse

the measure of an exterior angle of a triangle is greater in…

if p, then q

if q, then p

if not p, then not q

exterior angle inequality theorem

the measure of an exterior angle of a triangle is greater in…

statement

if p, then q