#### Study sets matching "honors theorems postulates geometry postulates theorems"

#### Study sets matching "honors theorems postulates geometry postulates theorems"

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

AAA Similarity Polstulate

SAS Similarity Theorem

SSS Similarity Theorem

Triangle Proportionality Theorem

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

If an angle of one triangle is congruent to an angle of anthe…

If the corresponding sides of two triangles are in proportion…

If a line parallel to a side of a triangle intersects the oth…

AAA Similarity Polstulate

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

SAS Similarity Theorem

If an angle of one triangle is congruent to an angle of anthe…

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

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

Through any two points, there is exactly one line.

Lines can only intersect at exactly one point.

Planes can only intersect at exactly one line.

Through any three non-collinear points, there is exactly one…

Postulate 1-1

Through any two points, there is exactly one line.

Postulate 1-2

Lines can only intersect at exactly one point.

right angles congruence theorem

congruent supplements theorem

congruent complements theorem

linear pairs 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…

the parallel postulate

theorem 16

theorem 17

corollary to theorem 17 : 1

through a point not on a line, there is exactly one line para…

in a plane, two points each equidistant from the endpoints of…

equal corresponding angles mean lines are parallel

equal alternate interior angles mean lines are parallel

the parallel postulate

through a point not on a line, there is exactly one line para…

theorem 16

in a plane, two points each equidistant from the endpoints of…

Linear Pair Theorem

Congruent Supplements Theorem

Right Angle Congruence Theorem

Congruent Complements Theorem

If 2 angles form a linear pair, then they are supplementary

If 2 angles are supplements of congruent angles or the same a…

If 2 angles are right angles then they are congruent

if two angles are complementary to the same angle or congruen…

Linear Pair Theorem

If 2 angles form a linear pair, then they are supplementary

Congruent Supplements Theorem

If 2 angles are supplements of congruent angles or the same a…

they are congruent.... Right Angles Cong…

Congruent Supplements Theorem

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 they…

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

Congruent Supplements Theorem

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

Corresponding Angles Postulate

Alternate Interior Angles Theorem

Alternate Exterior Angles Theorem

Consecutive 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 pair…

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

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…

Postulate "#5"

Postulate "#6"

Postulate "#7"

Postulate "#8"

A line contains at least 2 points.... A plane contains at least…

Through any two points there is exactly one line.

Through any three points there is at least one plane.... Through…

If two points are in a plane, the line that contains those po…

Postulate "#5"

A line contains at least 2 points.... A plane contains at least…

Postulate "#6"

Through any two points there is exactly one line.

Theorem 4.1 (Angle Sum Theorem)

Theorem 4.2 (Exterior Angles Theorem)

Corollary 4.1

Corollary 4.2

all three angles of a triangle equal 180 degrees

The exterior angle is equal to the sum of the 2 remote interi…

In a right triangle, the 2 acute angles are complementary

A triangle can have at most one right angle or one obtuse angle

Theorem 4.1 (Angle Sum Theorem)

all three angles of a triangle equal 180 degrees

Theorem 4.2 (Exterior Angles Theorem)

The exterior angle is equal to the sum of the 2 remote interi…

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…

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

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

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.

Math

Geometry

Conjecture

Inductive reasoning

The Science of patterns

The science of visual patterns

An unproven statement based on observations

A reasoning process that involved looking for patterns and ma…

Math

The Science of patterns

Geometry

The science of visual patterns

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

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

Polygons whose corresponding parts are…

The same or equal.

If two angles of one triangle are cong…

If three sides of one triangle are con…

Congruent Polygons

Congruent

Triangle Third Angle Sum Theorem

SSS Congruence Postulate

Polygons whose corresponding parts are…

Congruent Polygons

The same or equal.

Congruent

Theorem 5.3 (Circumcenter Theorem)

Theorem 5.4 (Angle Bisector Theorem)

Theorem 5.5 (Converse of the Angle Bis…

Theorem 5.6 (Incenter Theorem)

The perpendicular bisectors of a triangle intersect at a poin…

If a point is on the bisectors of an angle, then it is equidi…

If a point in the interior of an angle is equidistant from th…

The angle bisectors of a triangle intersect at a point called…

Theorem 5.3 (Circumcenter Theorem)

The perpendicular bisectors of a triangle intersect at a poin…

Theorem 5.4 (Angle Bisector Theorem)

If a point is on the bisectors of an angle, then it is equidi…

What are the five ways to prove a shap…

If two lines are parallel

If three parallel lines cut off congru…

A line that contains the midpoint of o…

1.) if both pairs of opposite sides of a quadrilateral are co…

then all the points on one line are equidistant from the othe…

then they cut off congruent segments on every transversal

passes through the midpoint of the third side

What are the five ways to prove a shap…

1.) if both pairs of opposite sides of a quadrilateral are co…

If two lines are parallel

then all the points on one line are equidistant from the othe…

Point

Line

plane

Co-linear points

a location in space

an infinite set of points strung together in one dimension

an infinite set of points strung together to form a boundless…

points that lie on the same line

Point

a location in space

Line

an infinite set of points strung together in one dimension

Dimension Postulate

Straight Line Postulate

Plane Existence Postulate

Flat Plane Postulate

A line contains at least 2 points... A plane contains at least 3…

Through any 2 distinct points there is exactly 1 line... 2 disti…

Through any 3 points there is at least 1 plane... 3 noncollinear…

If 2 points are in a plane, then the line that contains them…

Dimension Postulate

A line contains at least 2 points... A plane contains at least 3…

Straight Line Postulate

Through any 2 distinct points there is exactly 1 line... 2 disti…

Segment Addition Postulate

Supplement Theorem

Complement Theorem

Congruent Complements theorem

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

if 2 angles form a linear pair, then they are supplementary a…

If the noncommon sides of 2 adjacent angles form a right angl…

if <1+<2=180 and <2+<3=180, then <1 congruent to <3

Segment Addition Postulate

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

Supplement Theorem

if 2 angles form a linear pair, then they are supplementary a…

ruler postulate

segment addition postulate

protractor postulate

angle addition postulate

the points on a line can be paired with the real numbers in s…

if B is between A and C, than AB+BC= AC

ruler postulate w angles

if point B lies in the interior of ∠AOC than m∠AOB + m∠BOC =…

ruler postulate

the points on a line can be paired with the real numbers in s…

segment addition postulate

if B is between A and C, than AB+BC= AC

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 a•c=b•c

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

Point

Line

Plane

Collinear Points

A location in space

An infinite set of points strung together in one dimension

An infinite set of points strung together to form a boundless…

Points that lie on the same line

Point

A location in space

Line

An infinite set of points strung together in one dimension

Parallel Postulate

Perpendicular Postulate

Corresponding Angles Theorem

Alternate Interior Angles Theorem

If there is a line and a point not on the line, then there is…

If there is a line and a point not on the line, then there is…

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

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

Parallel Postulate

If there is a line and a point not on the line, then there is…

Perpendicular Postulate

If there is a line and a point not on the line, then there is…

If c^2=a^2=b^2, then the triangle is a…

A=½h(b₁=b₂)

The measure of the arc formed by two a…

Length of ArcAB=mArcAB/360*2πr

Converse of the Pythagorean Theorem

Area of a Trapezoid

Arc Addition Postulate

Arc Length

If c^2=a^2=b^2, then the triangle is a…

Converse of the Pythagorean Theorem

A=½h(b₁=b₂)

Area of a Trapezoid

Conditional

Converse

Inverse

Contrapositive

p→q; if p then q; equivalent to Contrapositive

q→p; if q then p; equivalent to Inverse

~p→~q; if not p then not q; equivalent to Converse

~q→~p; if not q then not p; equivalent to Conditional

Conditional

p→q; if p then q; equivalent to Contrapositive

Converse

q→p; if q then p; equivalent to Inverse

A(n) _________ is the part of a line c…

Two segments with the same lengths are…

A(n) __________ of a segment is the po…

A(n) __________ is a ray that divides…

segment

congruent

midpoint

angle bisector

A(n) _________ is the part of a line c…

segment

Two segments with the same lengths are…

congruent

Undefined Terms

Segment AB

Ray AB

The Line Postulate

Points, Lines, and Planes

Consists of points A and B and all the points in between them

Consists of segment AB and all points C such that B is betwee…

Through any two points there is exactly one line

Undefined Terms

Points, Lines, and Planes

Segment AB

Consists of points A and B and all the points in between them

Theorem 6.1 (Sum of Interior Angles of…

Theorem 6.2 (Sum of Exterior Angles of…

Theorem 6.3

Theorem 6.4

The sum of the interior angles of a convex polygon is represe…

The sum of the exterior angles of a convex polygon will alway…

Opposite sides of a parallelogram are congruent

Opposite angles of a parallelogram are congruent

Theorem 6.1 (Sum of Interior Angles of…

The sum of the interior angles of a convex polygon is represe…

Theorem 6.2 (Sum of Exterior Angles of…

The sum of the exterior angles of a convex polygon will alway…

The Ruler Postulate

The Protractor Postulate

The Betweenness of Points Theorem

The Betweenness of Rays Theorem

The points on a line can be numbered so that positive number…

The rays in a half rotation can be numbered from 0 to 180 so…

If A-B-C, then AB+BC=AC

If OA-OB-OC, then aAOB+aBOC=aAOC

The Ruler Postulate

The points on a line can be numbered so that positive number…

The Protractor Postulate

The rays in a half rotation can be numbered from 0 to 180 so…

law of detachment

law of syllogism

postulate 5

postulate 6

if P implies Q is a true conditional statement and P is true,…

if P implies Q and Q implies R is true, then P implies R.

through any two points there exists exactly one line.

a line contains at least two points.

law of detachment

if P implies Q is a true conditional statement and P is true,…

law of syllogism

if P implies Q and Q implies R is true, then P implies R.

Definition of right angles

Definition of straight angles

Definition of congruent angles

If 2 angles are right

If an angle is right, it is 90 degrees

If an angle is straight, it is 180 degrees

If 2 angles have the same measure, then they are congruent

then they are congruent

Definition of right angles

If an angle is right, it is 90 degrees

Definition of straight angles

If an angle is straight, it is 180 degrees

segment addition postulate

angle addition postulate

Post. 5: A line contains at least ____…

Post 5: A plane contains at least ____…

ex: If B is between points A and C then AB + BC = AC (pieces…

ex: if point B lies in the interior of <AOC then m<AOB + <BOC…

two

three

segment addition postulate

ex: If B is between points A and C then AB + BC = AC (pieces…

angle addition postulate

ex: if point B lies in the interior of <AOC then m<AOB + <BOC…

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 (a)(c) = (b)(c)

If a = b, c not equal to "zero", 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

Segment Addition Postulate

AM + MB = AB

Definition of a Midpoint

If M is the midpoint of AB, then AM = MB

AM + MB = AB

Segment Addition Postulate

If M is the midpoint of AB, then AM = MB

Definition of a Midpoint

Segment Addition Postulate

AM + MB = AB

AM + MB = AB

Segment Addition Postulate

point

Line

Plane

Collinear

represents a particular location. That which has no part.

an infinite collection of points in one dimension- that which…

an infinite collection in two dimension - that which has leng…

3 Points are collinear iff they are on the same line

point

represents a particular location. That which has no part.

Line

an infinite collection of points in one dimension- that which…

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…

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…

Radius

Chords

Tangents

Arcs

In a circle, a radius perpendicular to a chord bisects the ch…

In a circle, or congruent circles, congruent chords are equid…

Tangent segments to a circle from the same external point are…

In the same circle, or congruent circles, congruent central a…

Radius

In a circle, a radius perpendicular to a chord bisects the ch…

Chords

In a circle, or congruent circles, congruent chords are equid…

parallel pos.

perpendicular pos.

paragraph proof

transitive property of parallel lines

if there is a line and a point not on that line then there is…

if there is a line and a point not on that line then there is…

a proof written as a paragraph

if two lines are parallel to the same line then they are para…

parallel pos.

if there is a line and a point not on that line then there is…

perpendicular pos.

if there is a line and a point not on that line then there is…

theorem

postulate

definition

geometry

a statement that can be proved

something we don't need to prove, uses past information to ba…

assigns a term to an object. are always reversible

to take a series of facts to put in a logical way to reach a…

theorem

a statement that can be proved

postulate

something we don't need to prove, uses past information to ba…

Reflexive property

Symmetric property

Transitive property

Addition postulate

A quantity is congruent to itself

If a=b then b=a

If a=b and b=c then a=c

If equal quantities are added to equal quantities the sums ar…

Reflexive property

A quantity is congruent to itself

Symmetric property

If a=b then b=a

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

Protractor Postulate

Angle Addition Postulate

Line Postulate

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

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

If point B lies in the interior of ∠AOC, then the m∠AOB and t…

A line contains at least 2 points

Segment Addition Postulate

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

Protractor Postulate

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