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Congruent Polygons

Corollary

Equilateral Triangle

Isosceles Triangle

Polygons that have corresponding sides congruent and correspo…

Theorem that can proved easily using another theorem.

A triangle whose sides are all congruent.

Triangle that has two congruent sides.

Congruent Polygons

Polygons that have corresponding sides congruent and correspo…

Corollary

Theorem that can proved easily using another theorem.

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…

Postulate 1

Postulate 4

Postulate 5

Postulate 6

(Segment Addition Postulate)... if B is between A and C, then AB…

(Angle Addition Postulate)... if B lies in the interior of <AOC,…

a LINE contains at least 2 POINTS... a PLANE contains at least 3…

through any 2 POINTS there is exactly 1 LINE

Postulate 1

(Segment Addition Postulate)... if B is between A and C, then AB…

Postulate 4

(Angle Addition Postulate)... if B lies in the interior of <AOC,…

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…

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

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 alternat…

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 alternat…

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 alternat…

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 alternat…

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

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.

Through any two points,

Through any three noncollinear points,

A line contains at least

A plane contains at least

there is exactly one line.

there is exactly one plane.

two points.

three noncollinear points.

Through any two points,

there is exactly one line.

Through any three noncollinear points,

there is exactly one plane.

Segment Addition Postulate

Angle Addition Postulate

(Postulate) Through any two points

(Postulate) A line contains

If C is in the middle of line AB, then AC+CB=AC

If D is in the interior of ∠ABC, then m∠ABD + m∠DBC= m∠ABC

exists exactly one line

at least two points

Segment Addition Postulate

If C is in the middle of line AB, then AC+CB=AC

Angle Addition Postulate

If D is in the interior of ∠ABC, then m∠ABD + m∠DBC= m∠ABC

theorem

postulate

definition

segment bisector

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

segment,ray,line, plane that divides a segment into two congr…

theorem

a statement that can be proved

postulate

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

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…

Slope-Intercept Form (most graph-able…

Point-Slope Form (to get a point and s…

Slope of Two Points

Midpoint of a Line

y=mx+b

y-y₁=m(x-x₁)

Y₂-Y₁ / X₂-X₁

(x₁+x₂ / 2) , (y₁+y₂ / 2)

Slope-Intercept Form (most graph-able…

y=mx+b

Point-Slope Form (to get a point and s…

y-y₁=m(x-x₁)

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

coordinate midpoint property

segment additive property

angle addition property

linear pair theorem

if B is between A & C,... then AB+BC=AC

if D is on the interior of Angle ABC,... then m Angle ABD + m An…

if two angles form a linear pair,... then the two angles are sup…

coordinate midpoint property

segment additive property

if B is between A & 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 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

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…

Reflexive property

Symmetric propetry

Transitive property

Midpoint theorm

A=A, AB=AB, m<1=m<1

If A=B, then B=A. If AB=CD, then CD=AB

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

If M is the midpoint of segment AB, then AM= 1/2 AB

Reflexive property

A=A, AB=AB, m<1=m<1

Symmetric propetry

If A=B, then B=A. If AB=CD, then CD=AB

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Addition Property of Equality

a = a

If a = b... Then b = a

If a = b, and b = c ... Then a = c

If a = b ... Then a + 3 = b + 3

Reflexive Property of Equality

a = a

Symmetric Property of Equality

If a = b... Then b = a

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.

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

A/B=C/D is equal to

AA similarity postulate

SAS similarity postulate

SSS similarity postulate

cross multiplication (ad=bc), reciprocals (b/a d/c), numerato…

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

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

If the sides of two triangles are in proportion, then the tri…

A/B=C/D is equal to

cross multiplication (ad=bc), reciprocals (b/a d/c), numerato…

AA similarity postulate

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

midsegment of a triangle

Midsegment Theorem

coordinate proof

perpendicular bisector

a segment that connects the midpoints of two sides of a trian…

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

A proof involving placing geometric figures in a coordinate p…

A segment, ray, line, or plane that is perpendicular to a seg…

midsegment of a triangle

a segment that connects the midpoints of two sides of a trian…

Midsegment Theorem

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

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

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

point

line

plane

space

location, without size, represented by a dot -Notation: one s…

extends in two directions without ending; has no thickness -n…

suggested by a floor or wall; extends forever and has no thic…

set of all points (3D)

point

location, without size, represented by a dot -Notation: one s…

line

extends in two directions without ending; has no thickness -n…

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…

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

through any 2 points, there is exactly 1 line

through any 3 points not on the same line (noncollinear), the…

a line contains at least 2 points

a plane contains at least 3 points not on the same line (nonc…

Postulate 2.1

through any 2 points, there is exactly 1 line

Postulate 2.2

through any 3 points not on the same line (noncollinear), the…

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.

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…

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…

Point 1.1

Line 1.1

Plane 1.1

Collinear Points 1.1

A location in space.... 1.) Point has no dimension... 2.) Point is…

An infinite set of points strung together in one dimension.... 1…

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

Points that lie on the same line.

Point 1.1

A location in space.... 1.) Point has no dimension... 2.) Point is…

Line 1.1

An infinite set of points strung together in one dimension.... 1…

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

Postulate 3-1 Same-side Interior Angle…

Theorem 3-1 Alternate Interior Angles…

Theorem 3-2 Corresponding Angles Theor…

Theorem 3-3 Alternate Exterior Angles…

supplementary... m∠1 + m∠2 = 180

congruent

corresponding

exterior

Postulate 3-1 Same-side Interior Angle…

supplementary... m∠1 + m∠2 = 180

Theorem 3-1 Alternate Interior Angles…

congruent

segment

congruent

midpoint

angle bisector

a _______ is the part of a line consisting of two endpoints a…

two segments with the same length are _________

a ________ of a segment is the point that divides the segment…

an _____ ________ is a ray that divides an angle into two con…

segment

a _______ is the part of a line consisting of two endpoints a…

congruent

two segments with the same length are _________

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…

Postulate 1

Postulate 2

Postulate 3

Postulate 4

Ruler Postulate: The points on a line can be paired with the…

Segment Addition Postulate: If B is between A and C, then AB…

Protractor Postulate: On line AB in a given plane, choose any…

Angle Addition Postulate: If point B lies in the interior of…

Postulate 1

Ruler Postulate: The points on a line can be paired with the…

Postulate 2

Segment Addition Postulate: If B is between A and C, then AB…

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

Through any 2 points there is 1 line

If 2 distinct lines intersect, they will intersect at exactly…

If 2 distinct planes intersect, they will intersect at exactl…

Through any 3 noncollinear points there is exactly 1 plane

Postulate 1-1

Through any 2 points there is 1 line

Postulate 1-2

If 2 distinct lines intersect, they will intersect at exactly…

corresponding angles postulate

alternate interior angles theorem

alternate exterior angle theorem

consecutive (same-side) interior angle…

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

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

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

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

corresponding angles postulate

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

alternate interior angles theorem

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

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

On Line AB in a given plane, choose any point between A and B…

If Point B lies in the interior of Angle AOC, then the measur…

Ruler Postulate

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

Segment Addition Postulate

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

If two sides of a triangle are congrue…

If a transversal intersects two parall…

vertical angles are ________

The point of concurrency of the three…

base angles

congruent

congruent

incenter

If two sides of a triangle are congrue…

base angles

If a transversal intersects two parall…

congruent

corresponding angles postulate

converse of corresponding angles postu…

alternate interior angles theorem

converse of alternate interior angles…

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

if two coplanar lines are cut by a transversal so that a pair…

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

if two coplanar lines are cut by a transversal so that a pair…

corresponding angles postulate

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

converse of corresponding angles postu…

if two coplanar lines are cut by a transversal so that a pair…

Ruler Postulate

Angle defintion

Protractor Postulate

Angle Addition Postulate

There is a point on the number line for every real number.

An angle is formed by two rays with the same endpoint. The ra…

Any angle can be measured by a protractor.

Adding two angles to make a bigger angle.

Ruler Postulate

There is a point on the number line for every real number.

Angle defintion

An angle is formed by two rays with the same endpoint. The ra…

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 the AB + BC = AC. IF AB + BC = AC, th…

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

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 the AB + BC = AC. IF AB + BC = AC, th…

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

Median of a Triangle

Concurrent

Angle Bisector of a Triangle

Altitudes of a Triangle

a segment from a vertex of a triangle to the midpoint of the…

three lines intersecting at the same point

a segment from vertex to side opposite such that the angle is…

a segment from vertex to side opposite of the vertex such tha…

Median of a Triangle

a segment from a vertex of a triangle to the midpoint of the…

Concurrent

three lines intersecting at the same point