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postulate 1-1

postulate 1-2

postulate 1-3

postulate 1-4

through any two points there is exactly one line

if two distinct lines intersect, then they intersect in exact…

if two distinct planes intersect, then they intersect in exac…

through any three non-collinear points there is exactly one p…

postulate 1-1

through any two points there is exactly one line

postulate 1-2

if two distinct lines intersect, then they intersect in exact…

The ruler postulate

Segment addition postulate

Protractor postulate

Angle addition postulate

The points on a line can be put into one-to-one correspondenc…

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

Given line AB and point O on line AB, all rays that can be dr…

If S is in the interior of angle PQR, then measure of angle P…

The ruler postulate

The points on a line can be put into one-to-one correspondenc…

Segment addition postulate

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

HL congruence theorem

SSS

ASA

SAS

If the hypotenuse and a leg of a right triangle are congruent…

If all the sides are congruent

Two angles and the included side is congruent

Two sides and the included angle are congruent

HL congruence theorem

If the hypotenuse and a leg of a right triangle are congruent…

SSS

If all the sides are congruent

expansion

line

flat plane

plane intersection

Which postulate states that a line contains at least two poin…

Which postulate states that any two points in space lie in ex…

Which postulate states if two points lie in a plane, then the…

Which postulate states if two planes intersect, then their in…

expansion

Which postulate states that a line contains at least two poin…

line

Which postulate states that any two points in space lie in ex…

reflexive property

symmetric property

transitive of equality (inequality)

communative with respect to addition

If x=x, then x=x.

If x=y, then y=x.

If x=y and y=z, then x=z. (same for inequality)

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

reflexive property

If x=x, then x=x.

symmetric property

If x=y, then y=x.

Def. of Congruent

Def. of Midpoint

Def. of Segment bisector

Def. of Acute angle

If 2 segments, or angles equal each other they are congruent.

A point on a line segment that divides it into two equal parts.

A line, ray or segment which cuts another line segment into t…

An angle that is less than 90 degrees.

Def. of Congruent

If 2 segments, or angles equal each other they are congruent.

Def. of Midpoint

A point on a line segment that divides it into two equal parts.

Congruent Supplements Theorem

Congruent Complements Theorem

Linear Pair Postulate

Vertical Angle Theorem

If two angles are supplementary to the same or congruent angl…

If two angles are complementary to the same or congruent angl…

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

Vertical angles are congruent

Congruent Supplements Theorem

If two angles are supplementary to the same or congruent angl…

Congruent Complements Theorem

If two angles are complementary to the same or congruent angl…

Postulate One (Ruler Postulate)

Postulate Two (Segment Addition Postul…

Postulate Three (Protractor Postulate)

Postulate Four (Angle Addition Postula…

The points on a line can be paired with the real numbers so t…

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

On line AB, choose any point O between A and B. Ray OA is pai…

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

Postulate One (Ruler Postulate)

The points on a line can be paired with the real numbers so t…

Postulate Two (Segment Addition Postul…

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

inductive reasoning

conjecture

counterexample

conditional

the observance of a pattern in order to form a conclusion

the conclusion you reach through inductive reasoning

an example that proves something false

sentence written in if-then format

inductive reasoning

the observance of a pattern in order to form a conclusion

conjecture

the conclusion you reach through inductive reasoning

Adjacent Angles

Bisector of an angle

Bisector of a segment

Collinear points

Two angles in a plane that have a common vertex and a common…

The ray that divides the angle into two congruent adjacent an…

A line, segment, ray or plane that intersects the segment at…

Points all in one line.

Adjacent Angles

Two angles in a plane that have a common vertex and a common…

Bisector of an angle

The ray that divides the angle into two congruent adjacent an…

Theorem 4.1

Theorem 4.2

Theorem 4.3

Corollary 4.1

Angle Sum Theorem- The sum of the measures of the angles of a…

Third Angle Theorem- If two angles of one triangle are congru…

Exterior Angle Theorem- The measure of an exterior angle of a…

The acute angles of a right triangle are complementary.

Theorem 4.1

Angle Sum Theorem- The sum of the measures of the angles of a…

Theorem 4.2

Third Angle Theorem- If two angles of one triangle are congru…

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

Midpoint Theorem

Linear Pair Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

If M is the midpoint of ĀB, then ĀM~MB

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

If two angles are supplementary to the same angle (or two con…

If two angles are complementary to the same angle (or two con…

Midpoint Theorem

If M is the midpoint of ĀB, then ĀM~MB

Linear Pair Theorem

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

Complementary Angles

Supplementary Angles

Theorem

Vertical Angles

Two angles whose measures have a sum of 90

Two angles whose measures have a sum of 180

A statement that can be proven

Tow angles formed by intersecting lines and facing in the opp…

Complementary Angles

Two angles whose measures have a sum of 90

Supplementary Angles

Two angles whose measures have a sum of 180

Segment addition postulate

Angle addition postulate

Two point postulate

Line point postulate

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

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

Through any two points, there exists exactly one line.

A line contains at least two points.

Segment addition postulate

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

Angle addition postulate

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

Reflexive Property

Side Side Side

Side Angle Side

Angle Side Angle

Any segment or angle is congruent to itself

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 include side of one triangle are congru…

Reflexive Property

Any segment or angle is congruent to itself

Side Side Side

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

reflexive postulate

addition postulate

subtraction postulate

substitution postulate

A quantity is congruent to itself a=a.

If equal quantities are added to equals quantities, the sums…

If equal quantities are subtracted from equal quantities, the…

A quantity may be substituted for its equal in any expression.

reflexive postulate

A quantity is congruent to itself a=a.

addition postulate

If equal quantities are added to equals quantities, the sums…

Point

Line

Plane

Segment

Has no dimension. Represented by a dot

Has one dimension. Represented by a line with two arrowheads,…

Has two dimensions. Represented by a shape that looks like a…

Consists of two endpoints and all points between the two endp…

Point

Has no dimension. Represented by a dot

Line

Has one dimension. Represented by a line with two arrowheads,…

Corresponding angles postulate

Alternate interior angles theorem

Same-side interior angles theorem

Alternate exterior angles theorem

If a transversal intersects two parallel lines, then correspo…

If a transversal intersects two parallel lines, then the alte…

If a transversal intersects two parallel lines, then same-sid…

If a transversal intersects two parallel lines, then alternat…

Corresponding angles postulate

If a transversal intersects two parallel lines, then correspo…

Alternate interior angles theorem

If a transversal intersects two parallel lines, then the alte…

Congruent Complements Theorem

Right Angle Congruence Theorem

Vertical Angles Theorem

Corresponding Angles Postulate

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

All right angles are congruent

If two angles are vertical angles, then they are congruent

Corresponding angle pairs are congruent

Congruent Complements Theorem

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

Right Angle Congruence Theorem

All right angles are congruent

Acute Angle

Angle

Angle Bisector

Axiom

An angle is acute, if and only if, it has a measure greater t…

Two rays, or segments, with the same endpoint form an angle.

A ray that divides an angle into two congruent angles.

An accepted statement of fact; postulate.

Acute Angle

An angle is acute, if and only if, it has a measure greater t…

Angle

Two rays, or segments, with the same endpoint form an angle.

Corresponding Angles Postulate

Alternate Interior Angles Theorem

Alternate Exterior Angles Theorem

Same-side Interior Angles Theorem

corresponding angles are congruent

alternate interior angles are congruent

alternate exterior angles are congruent

same-side interior angles are supplementary

Corresponding Angles Postulate

corresponding angles are congruent

Alternate Interior Angles Theorem

alternate interior angles are congruent

if M is the midpoint of AB

through a line and a point not in the…

if two lines intersect

if BX is the bisector of angle ABC

AM = 1/2AB and MB = 1/2 AM

there is exactly one plane

exactly one plane contains the lines

measurement of angle ABX = 1/2 measurement of angle ABC

if M is the midpoint of AB

AM = 1/2AB and MB = 1/2 AM

through a line and a point not in the…

there is exactly one plane

side XY is congruent to side XZ

Triangle Sum Thm.

Isosceles Triangle Thm.

two congruent sides

Since XY equals XZ

M<X + M<Y + M<Z = 180

base angles Z & Y are congruent so m<Z = M<Y

Isosceles Triangles have at least

side XY is congruent to side XZ

Since XY equals XZ

Triangle Sum Thm.

M<X + M<Y + M<Z = 180

Postulate 5

Postulate 6

Postulate 8

Postulate 9

Through any 2 points there exists exactly one line

A line contains at least 2 points

Through any 3 non-collinear points there exists exactly one p…

A plane contains at least 3 noncollinear points

Postulate 5

Through any 2 points there exists exactly one line

Postulate 6

A line contains at least 2 points

Vertical Angle Theorem

Adjacent Angle

Complementary Angle

Supplementary angle

Vertical Angles are congruent

A pair of angles in the same plane that meet the following co…

2 angles whose measures add up to 90 degrees

2 angles whose measures add up to 180 degrees

Vertical Angle Theorem

Vertical Angles are congruent

Adjacent Angle

A pair of angles in the same plane that meet the following co…

If there are two points,

If there is a line,

Two points determine a ____

If there are three noncollinear points,

there is exactly one line that contains them.

then there are at least two points on the line

line

there is exactly one plane that contains them

If there are two points,

there is exactly one line that contains them.

If there is a line,

then there are at least two points on the line

Segment Addition Postulate

Alternate Interior Angles Theorem

Same Side Interior Angles Theorem

Alternate Exterior Angles Thereom

If 3 points A, B, and C are collinear and B is between A and…

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

If 2 parallel lines in a plane are cut by a transversal line,…

If 2 parallel lines are cut by a transversal, then alternate…

Segment Addition Postulate

If 3 points A, B, and C are collinear and B is between A and…

Alternate Interior Angles Theorem

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

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

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Perpendicular Lines

A=A

A=B... B=A

If A=B & B=C, then A=C

Lines that intersect and form right angles

Reflexive Property of Equality

A=A

Symmetric Property of Equality

A=B... B=A

Addition Property

Subtraction Property

Multiplication Property

Division Property

Adding on both sides of the equal sign

Subtracting on both sides of the equal sign

Multiplying on both sides of the equal sign

Dividing on both sides of the equal sign

Addition Property

Adding on both sides of the equal sign

Subtraction Property

Subtracting on both sides of the equal sign

Linear Pair Theorem

Congruent Supplement Theorem

Right Angle Congruence Theorem

Congruent Complementary Theorem

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

If two angles are supplementary to the same angle (or to two…

All right angles are congruent

If two angles are complementary to the same angle (or two con…

Linear Pair Theorem

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

Congruent Supplement Theorem

If two angles are supplementary to the same angle (or to two…

Addition Propery 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 a•c=b•c

If a=b, then a÷c=b÷c

Addition Propery of Equality

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

Subtraction Property of Equality

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

Postulate 1-1:

Postulate 1-2:

Postulate 1-3:

Postulate 1-4:

Through any two points there is exactly one line

If two distinct lines intersect, then they intersect in exact…

If two distinct planes intersect, then they intersect in exac…

Through any three noncollinear points there is exactly one pl…

Postulate 1-1:

Through any two points there is exactly one line

Postulate 1-2:

If two distinct lines intersect, then they intersect in exact…

addition postulate

subtraction postulate

multiplication postulate

division postulate

if =/≅'s are added to =/≅, then the sums are =/≅

if =/≅'s are subtracted from =/≅'s, then the differences are…

if =/≅'s are multiplied by =/≅'s , then the products are =/≅

if =/≅'s are divided by =/≅'s then the quotients are =/≅

addition postulate

if =/≅'s are added to =/≅, then the sums are =/≅

subtraction postulate

if =/≅'s are subtracted from =/≅'s, then the differences are…

Angle Addition Postulate

Right Angle Congruence

Linear Pair Theorem

Vertical Angle Theorem

The measure of two smaller angles equals the measure of a lar…

All right angles are congruent.

If two angles are a linear pair (adjacent and make a line), t…

If two angles are vertical angles, then they are congruent.

Angle Addition Postulate

The measure of two smaller angles equals the measure of a lar…

Right Angle Congruence

All right angles are congruent.

right angles congruence theorem

congruent supplements theorem

congruent complements theorem

linear pair postulate

all right angles are congruent

if two angles are supplementary to the same angle (or to cong…

if two angles are complementary to the same angle (or to cong…

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

right angles congruence theorem

all right angles are congruent

congruent supplements theorem

if two angles are supplementary to the same angle (or to cong…

point

plane

line

collinear points

a location (undefined term)

a flat surface made up of points; has no depth and extends in…

made up of points and has no thickness or width (undefined te…

points on the same line

point

a location (undefined term)

plane

a flat surface made up of points; has no depth and extends in…

What is a net?

What is an isometric drawing?

What is an orthographic drawing?

What is a Point?

A net is a two-dimensional diagram that you can fold to form…

A drawing that shows a corner view of a 3D figure.

A drawing that shows the front, right, and top view of a 3D f…

indicates a location(is of no size value). Classified as the…

What is a net?

A net is a two-dimensional diagram that you can fold to form…

What is an isometric drawing?

A drawing that shows a corner view of a 3D figure.

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

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

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…

Postulate(1-1)

Postulate(1-2)

Postulate(1-3)

Postulate(1-4)

Through any two points there is exactly one line

If two distinct lines intersect, then they intersect in exact…

If two distinct planes intersect, then they intersect in exac…

Through any three noncollinear points there is exactly one pl…

Postulate(1-1)

Through any two points there is exactly one line

Postulate(1-2)

If two distinct lines intersect, then they intersect in exact…

Postulate 1 (Ruler Postulate)

Postulate 2 (Segment Addition Postulate)

Postulate 3 (Protractor Postulate)

Postulate 4 (Angle Addition Postulate)

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

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

If in <QOA, Ray OP lies inside of the angle, ... <QOP=<QOA-<POA

If point B lies on the interior of angle AOC, then angle AOB+…

Postulate 1 (Ruler Postulate)

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

Postulate 2 (Segment Addition Postulate)

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

midsegment theorem

perpendicular bisector theorem

converse of the perpendicular bisector…

concurrency of perpendicular bisectors…

the segment connecting the midpoints of two sides of a triang…

in a plane, if a point is on the perpendicular bisector of a…

in a plane, if a point is equidistant from the endpoints of a…

the perpendicular bisectors of a triangle intersect at a poin…

midsegment theorem

the segment connecting the midpoints of two sides of a triang…

perpendicular bisector theorem

in a plane, if a point is on the perpendicular bisector of a…

Right Angles Congruence Theorem

Midpoint Theorem

Ruler Postulate

Segment Addition Postulate

All right angles are congruent

If M is the midpoint of line segment AB, then line segment AM…

Given any 2 points A and B on a line, if A corresponds to 0,…

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

Right Angles Congruence Theorem

All right angles are congruent

Midpoint Theorem

If M is the midpoint of line segment AB, then line segment AM…

Reflexive Property Congruence

Symmetric Property Congruence

Transitive Property Congruence

Right Angles Congruence Theorem

If AB = AB, then AB = AB.

If AB = CD, then CD = AB.

If AB = CD and CD = EF, then AB = EF.

All right angles are congruent.

Reflexive Property Congruence

If AB = AB, then AB = AB.

Symmetric Property Congruence

If AB = CD, then CD = AB.

Triangle Sum Theorem

Exterior Angle Theorem

Corollary

Definition of Congruent Polygons

The sum of the measures of the interior angles of a triangle…

The measure of an exterior angle of a triangle is equal to th…

A statement that follows directly from a theorem.

Two shapes/figures are congruent if and only if all of their…

Triangle Sum Theorem

The sum of the measures of the interior angles of a triangle…

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to th…