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Right angle Thm( RAT).

Congruent supplements theorem (cst)

Linear pair postulate( llp)

Vertical angle theorem( VAT)

All right angles are congruent. Write they are right angles i…

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

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

Vertical angles are congruent.

Right angle Thm( RAT).

All right angles are congruent. Write they are right angles i…

Congruent supplements theorem (cst)

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

Thm 1.1

Thm 1.2

Thm 1.3

Thm 2.1

Two lines intersect at exactly one point

Through a line and a point not on the line, there is exactly…

If two lines intersect, then exactly one plane contains those…

Midpoint theorem

Thm 1.1

Two lines intersect at exactly one point

Thm 1.2

Through a line and a point not on the line, there is exactly…

Segment Addition Postulate

Same Side Interior Angle Theorem

Isosceles Triangle Theorem

No Choice Theorem / 3rd Angles Theorem

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

If two lines are cut by a transversal, the same side interior…

If two sides of a ∆ are congruent, then the angles opposite t…

If two angles of a ∆ are congruent to two angles of another ∆…

Segment Addition Postulate

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

Same Side Interior Angle Theorem

If two lines are cut by a transversal, the same side interior…

Segment Addition Postulate

Same Side Interior Angle Theorem

Isosceles Triangle Theorem

No Choice Theorem / 3rd Angles Theorem

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

If two lines are cut by a transversal, the same side interior…

If two sides of a ∆ are congruent, then the angles opposite t…

If two angles of a ∆ are congruent to two angles of another ∆…

Segment Addition Postulate

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

Same Side Interior Angle Theorem

If two lines are cut by a transversal, the same side interior…

vertical angles theorem

if two angles are supplements of the s…

if two angles are complements of the s…

all right angles are __________

vertical angles are congruent

congruent

congruent

congruent

vertical angles theorem

vertical angles are congruent

if two angles are supplements of the s…

congruent

1-1 Segment Addition Posulate

1-2 Definition:... ≅ seg

1-2 Definition:... Midpoint of a segment

1-3 Angle Addition Postulate

If point B is between G and S, then GB+BS=GS... If GB+BS=GS, the…

If 2 seg are ≅, then they have = length ... If 2 seg have the =…

If a pt is the MP of a segment, then it ÷s the segment into 2…

If point H is inside ∠GBS, then m∠GBH+m∠SBH=m∠GBS

1-1 Segment Addition Posulate

If point B is between G and S, then GB+BS=GS... If GB+BS=GS, the…

1-2 Definition:... ≅ seg

If 2 seg are ≅, then they have = length ... If 2 seg have the =…

The "Undefined Terms of Geometry"...

point

line

plane

point, line, plane

a location in space represented by a dot and usually assigned…

a straight path that extends without end in opposite directions

a flat surface that extends forever

The "Undefined Terms of Geometry"...

point, line, plane

point

a location in space represented by a dot and usually assigned…

Segment Addition Postulate

Angle Addition Postulate

Definition of Midpoint & Bisector

Definition of Angle Bisector

If B is between A and C then the length of AC is equal to the…

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

A bisector bisects a line segment at its midpoint which divid…

A ray that divides an angle into two adjacent angles that are…

Segment Addition Postulate

If B is between A and C then the length of AC is equal to the…

Angle Addition Postulate

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

Linear Pair Theorem

Vertical Angles Theorem

Corresponding Angles Theorem

Alt. Interior Angles Theorem

If two angles form a linear pair then add up to 180 degrees

If two angles are vertical then they are congruent

If 2 parallel lines cut by a transversal form 2 corresponding…

If 2 parallel lines cut by a transversal form 2 alt. interior…

Linear Pair Theorem

If two angles form a linear pair then add up to 180 degrees

Vertical Angles Theorem

If two angles are vertical then they are congruent

Right Angle Congruence Theorem

Congruent Supplement Theorem

Congruent Complements Theorem

Vertical Angles Congruence Theorem

all right angles are congruent... Given:∠1 +∠2 are right angles…

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

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

Vertical angles are congruent... Given: ∠1 and ∠2 are vertical ∠…

Right Angle Congruence Theorem

all right angles are congruent... Given:∠1 +∠2 are right angles…

Congruent Supplement Theorem

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

The "Undefined Terms of Geometry"...

point

line

plane

point, line, plane

a location in space represented by a dot and usually assigned…

a straight path that extends without end in opposite directions

a flat surface that extends forever

The "Undefined Terms of Geometry"...

point, line, plane

point

a location in space represented by a dot and usually assigned…

The "Undefined Terms of Geometry"...

point

line

plane

point, line, plane

a location in space represented by a dot and usually assigned…

a straight path that extends without end in opposite directions

a flat surface that extends forever

The "Undefined Terms of Geometry"...

point, line, plane

point

a location in space represented by a dot and usually assigned…

segment addition postulate

reflexive property

congruent

midpoint theorem

AB + BC = AC

any segment or angle is congruent/equal to itself (AB = AB) (…

have equal measure

If AB + BC = AC and AB=BC

segment addition postulate

AB + BC = AC

reflexive property

any segment or angle is congruent/equal to itself (AB = AB) (…

Theorem 2-1:Midpoint Theorem

Theorem 2-2:Angle Bisector Theorem

Theorem 2-3:

Theorem 2-4

If M is the midpoint of line AB, then = 1/2AB and MB = 1/2AB

If ray BX is the bisector of angle ABC, then the measure of a…

...

...

Theorem 2-1:Midpoint Theorem

If M is the midpoint of line AB, then = 1/2AB and MB = 1/2AB

Theorem 2-2:Angle Bisector Theorem

If ray BX is the bisector of angle ABC, then the measure of a…

Theorem #1

Theorem #2

Theorem #3

Theorem #4

If two adjacent angles form a right angle, then they are comp…

If two adjacent angles form a straight angle, then they are s…

If two angles are congruent, then their complements are congr…

If two angles are congruent, then their supplements are congr…

Theorem #1

If two adjacent angles form a right angle, then they are comp…

Theorem #2

If two adjacent angles form a straight angle, then they are s…

Theorem 24

Theorem 25

Theorem 26

Theorem 27:

If two points are each equidistant from the endpts of a seg,…

If a point is on the perpendicular bisector of a segment then…

If two nonvertical lines are parallel, then their slopes are…

If the slopes of two nonvertical lines are equal, then the li…

Theorem 24

If two points are each equidistant from the endpts of a seg,…

Theorem 25

If a point is on the perpendicular bisector of a segment then…

Theorem 1

Theorem 2

Theorem 4 (SSAC)

Theorem 5 (SCAC)

If two angles are right angles, then they are congruent

If two angles are straight angles, then they are congruent

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

If angles are supplementary to congruent angles, then they ar…

Theorem 1

If two angles are right angles, then they are congruent

Theorem 2

If two angles are straight angles, then they are congruent

Theorem 1- the betweenness of points t…

Theorem 2- the betweenness of rays the…

Theorem 3

Theorem 4

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

If OA-OB-OC, then <AOB + <BOC = <AOC

Complements of the same angle are equal

Supplements of the same angle are equal

Theorem 1- the betweenness of points t…

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

Theorem 2- the betweenness of rays the…

If OA-OB-OC, then <AOB + <BOC = <AOC

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

Right Angle Theorem

Vertical angles are congruent

If two angles are supplements of the same or congruent angle…

If two angles are compliments of the same or congruent angle…

All right angles are congruent

Vertical Angles Theorem

Vertical angles are congruent

Congruent Supplements Theorem

If two angles are supplements of the same or congruent angle…

Angle Add postulate

Supplement theorem

Complement theorem

Reflexive property of congruence

D is the interior of <ABC if and only if m<abc+m<dbc=ABC

If two angles form a linear pair then they are supplementary

If two no common sides of two adjacent angles form a right an…

Any angle is congruent to its self

Angle Add postulate

D is the interior of <ABC if and only if m<abc+m<dbc=ABC

Supplement theorem

If two angles form a linear pair then they are supplementary

SSS

SAS

ASA

AAS

if the sides of one triangle are congruent to the sides of a…

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 a non included side of one triangle are con…

SSS

if the sides of one triangle are congruent to the sides of a…

SAS

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

vertical angles theorem

congruent supplements theorem

congruent complements theorem

right angles theorem

if two angles are vertical then they are congruent

if two angles are supplements of the same angle then the two…

if two angles are complements of the same angle then the two…

if two angles are right then they are congruent

vertical angles theorem

if two angles are vertical then they are congruent

congruent supplements theorem

if two angles are supplements of the same angle then the two…

Congruent radii theorem

Congruent right angles theorem

Diameter midpoint theorem

Noncommon perpendicular ray complement…

If two line segments are the radii of the same Circle, then t…

If two angles are right angles, then they are congruent

The center of the circle is the midpoint of its diameter

If angles are adjacent with noncommon perpendicular rays, the…

Congruent radii theorem

If two line segments are the radii of the same Circle, then t…

Congruent right angles theorem

If two angles are right angles, then they are congruent

Same-side interior angle postulate

Alternate interior angles theorem

corresponding angles theorem

alternate exterior angles theorem

if a transversal intersects two parallel lines then same-side…

if a transversal intersects two parallel lines then alternate…

if a transversal intersects two parallel lines then correspon…

if a transversal intersects two parallel lines then alternate…

Same-side interior angle postulate

if a transversal intersects two parallel lines then same-side…

Alternate interior angles theorem

if a transversal intersects two parallel lines then alternate…

Reflexive Property

Midpoint Theorem

Vertical Angle Theorem

Alternate Interior Angle Theorem

For every real number, the number equals itself. Ex. x=x

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

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

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

Reflexive Property

For every real number, the number equals itself. Ex. x=x

Midpoint Theorem

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

Theorem 1

Theorem 2

Theorem 3

Theorem 4

Congruent complements measure 45 degrees

Complements of congruent angles are congruent

Supplements of the same angle are congruent

Two lines parallel to the same line are parallel to each other

Theorem 1

Congruent complements measure 45 degrees

Theorem 2

Complements of congruent angles are congruent

Theorem 2.1 (Congruent Supplements Thm.)

Theorem 2.2 (Congruent Complements Thm.)

Theorem 2.3 (Vertical Angles Thm.)

Theorem 3.1 (Transitivity of Parallel…

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

If two angles are complementary to the same angle or to congr…

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

If two lines are parallel to the same line, then they are par…

Theorem 2.1 (Congruent Supplements Thm.)

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

Theorem 2.2 (Congruent Complements Thm.)

If two angles are complementary to the same angle or to congr…

Perpendicular Bisector Thm

Conv. of Perpendicular Bisector Thm

Angle Bisector Thm

Conv. of Angle Bisector Thm

If a point is on the perpendicular bisector of a segment, the…

If a point is equidistant from the endpoints of a segment, th…

If a point is on the bisect of an angle, then it's equidistan…

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

Perpendicular Bisector Thm

If a point is on the perpendicular bisector of a segment, the…

Conv. of Perpendicular Bisector Thm

If a point is equidistant from the endpoints of a segment, th…

angle theorem

angle theorem

angle theorem

angle theorem

if 2 angles are supplementary to the same angle then they are…

if two angles are supplementary to congruent angles then they…

if two angles are complementary to the same angle then they a…

if two angles are complementary to congruent angles then they…

angle theorem

if 2 angles are supplementary to the same angle then they are…

angle theorem

if two angles are supplementary to congruent angles then they…

Theorem 1-1

Theorem 1-2

Theorem 1-3

Midpoint theorem

If two lines intersect then they intersect in exactly one point

Through a point and a point not on that line there is exactly…

If two lines intersect, then exactly one plane contains the l…

If M is the midpoint of segment AB the AM= 1/2AB and MB=1/2AB

Theorem 1-1

If two lines intersect then they intersect in exactly one point

Theorem 1-2

Through a point and a point not on that line there is exactly…

Corresponding Angles Posulate

Alternate Interior Angles postulate

Consecutive Interior Angles Postulate

Alternate Exterior Angles postulate

if two lines are cut by a transversal, then the pairs of C.A.…

if two lines are cut by a transversal, then the pairs of A.I.…

if two lines are cut by a transversal, then the pairs of A.E.…

if two lines are cut by a transversal, then the pairs of C.I.…

Corresponding Angles Posulate

if two lines are cut by a transversal, then the pairs of C.A.…

Alternate Interior Angles postulate

if two lines are cut by a transversal, then the pairs of A.I.…

Cpctc

Reflexive

Hypotenuse leg

Hypotenuse

Corresponding parts of congruent triangles are congruent

A value is equal to itself

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

the longest side of a right triangle, opposite the right angle

Cpctc

Corresponding parts of congruent triangles are congruent

Reflexive

A value is equal to itself

1

2

3

4

If two angles are right angles, then they are congruent

If two angles are straight angles then they are congruent

If a conditional statement is true, then the contrapositive o…

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

1

If two angles are right angles, then they are congruent

2

If two angles are straight angles then they are congruent

Right Angle

Congruent angles

Congruent Straight Angles

Bisecting

If an angle is a right angle, then its meausre is 90°

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

If two angles are straight angles, then they are congruent

If a line bisects an angle, then the two angles formed are co…

Right Angle

If an angle is a right angle, then its meausre is 90°

Congruent angles

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

theorem 1

theorem 2

theorem 3

theorem 4

if two angles are right angles, then they are congruent

if two angles are straight angles, then they are congruent

if a conditional statement is true, then the contrapositive o…

if angles are supplementary to the same angle, then they are…

theorem 1

if two angles are right angles, then they are congruent

theorem 2

if two angles are straight angles, then they are congruent

1-1

1-2

1-3

2-1

If two lines intersect, they intersect in exactly one point.

Through a line and a point not in that line, there is exactly…

If two lines intersect, then exactly one plane contains the l…

If M is the midpoint on segment AB, then AM = 1/2 AB and MB =…

1-1

If two lines intersect, they intersect in exactly one point.

1-2

Through a line and a point not in that line, there is exactly…

Theorem 9-4

Theorem 9-5

Theorem 9-6

Theorem 9-7

1) congruent arcs have congruent chords... 2) congruent chords h…

A diameter that is perpendicular to a chord bisects the chord…

In the same circle or congruent circles:... 1) chords equally di…

The measure of an inscribed angle is equal to half the measur…

Theorem 9-4

1) congruent arcs have congruent chords... 2) congruent chords h…

Theorem 9-5

A diameter that is perpendicular to a chord bisects the chord…

~ ( ~p) <=> p... 2 negatives make a posit…

p <=> p v p... p <=> p ^ p

p v q <=> q v p... p ^ q <=> q ^ p... Switch…

(p v q) v r <=> p v (q v r)... (p ^ q) ^…

double negation

simplification

communitive theroms

associative theroms

~ ( ~p) <=> p... 2 negatives make a posit…

double negation

p <=> p v p... p <=> p ^ p

simplification

Linear Pair Theorem

Vertical Angles Theorem

Corresponding Angles Theorem

Alt. Interior Angles Theorem

If two angles form a linear pair then add up to 180 degrees

If two angles are vertical then they are congruent

If 2 parallel lines cut by a transversal form 2 corresponding…

If 2 parallel lines cut by a transversal form 2 alt. interior…

Linear Pair Theorem

If two angles form a linear pair then add up to 180 degrees

Vertical Angles Theorem

If two angles are vertical then they are congruent

1

2

3

4

If two angles form a right angle, then they are complementary

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

If two angles are complements of the same angle, then they ar…

If two angles are congruent, then their complements are congr…

1

If two angles form a right angle, then they are complementary

2

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

Theorem 1

Theorem 2

Theorem 3

Theorem 4

If two angles are right angles, then they are congruent (Righ…

If two angle are straight angles, then they are congruent (St…

If a conditional statement is true, then its contrapositive i…

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

Theorem 1

If two angles are right angles, then they are congruent (Righ…

Theorem 2

If two angle are straight angles, then they are congruent (St…

IAT

SIAT

DIAT

CQT

inscribed angle theorem (two inscribed angles subtending same…

sector inscribed angle theorem (a sector angle subtending the…

diameter inscribed angle theorem (an inscribed angle subtende…

cyclic quadrilateral theorem (opposite angles of a cyclic qua…

IAT

inscribed angle theorem (two inscribed angles subtending same…

SIAT

sector inscribed angle theorem (a sector angle subtending the…