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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 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…

Right Angle Congruence Theorem

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

If 2 angles are right angles, then they are congruent

If 2 angles are vertical angles, then they are congruent

If 2 angles are supplementary to the same angle or congruent…

If 2 angles are complementary to the same angle or congruent…

Right Angle Congruence Theorem

If 2 angles are right angles, then they are congruent

Vertical Angles Theorem

If 2 angles are vertical angles, then they are congruent

Triangle Sum Theorem

Corollary to the Triangle Sum Theorem

Exterior Angles Theorem

Third Angles Theorem

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

The acute angles of a right triangle are complementary.

The measure of an exterior angle of a triangle equals the sum…

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

Triangle Sum Theorem

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

Corollary to the Triangle Sum Theorem

The acute angles of a right triangle are complementary.

Same-side Interior Angle Postulate... If…

Alternate Interior Angles Theorem... If a…

Corresponding Angles Theorem... If a tran…

Alternate Exterior Angles Theorem... If a…

supplementary... m∠1 + m∠2 = 180

congruent

corresponding

exterior

Same-side Interior Angle Postulate... If…

supplementary... m∠1 + m∠2 = 180

Alternate Interior Angles Theorem... If a…

congruent

SSS

SAS

ASA

ITT

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

SSS

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

SAS

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

Theorem 4-1: Third Angles Theorem

Postulate 4-1: Side-Side-Side (SSS) Po…

Postulate 4-2: Side-Angle-Side (SAS) P…

Postulate 4-3: Angle-Side-Angle (ASA)…

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

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

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

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

Theorem 4-1: Third Angles Theorem

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

Postulate 4-1: Side-Side-Side (SSS) Po…

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

Third Angle Theorem

SSS (side-side-side)

SAS (side-Angle- side)

ASA (angle-side-angle)

If 2 angles of one triangle are congruent to two angles of an…

If the 3 sides of one triangle are congruent to the 3 sides o…

If 2 sides and the included angle of one triangle are congrue…

If 2 angles and the included side of one triangle are congrue…

Third Angle Theorem

If 2 angles of one triangle are congruent to two angles of an…

SSS (side-side-side)

If the 3 sides of one triangle are congruent to the 3 sides o…

Third Angles Theorem

Reflexive Property of Congruence

Side-Side-Side (SSS) Congruence

Side-Angle-Side (SAS) Congruence

If 2 angles of one triangle are congruent to 2 angles of a se…

When 2 triangles share a common side we use the ___________ t…

If 3 sides of one triangle are congruent to 3 sides of a 2nd…

If 2 sides and the INCLUDED angle of one triangle are congrue…

Third Angles Theorem

If 2 angles of one triangle are congruent to 2 angles of a se…

Reflexive Property of Congruence

When 2 triangles share a common side we use the ___________ t…

triangle sum theorem

exterior angles theorem

corollary to the triangle sum theorem

third angles theorem

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…

the acute angles of a right triangle are complementary

if two angles of one triangle are congruent tot two angles of…

triangle sum theorem

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

exterior angles theorem

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

Same-Side Interior Angles Postulate

Alternate Interior Angles Theorem

Corresponding Angles Theorem

Converse of the Same-Side Interior Ang…

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 lines are cut by a transversal so that a pair of same-…

Same-Side Interior 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 4.1 Triangle Sum Theorem

Theorem 4.2 Exterior Angle Theorem

Corollary to the Triangle Sum Theorem

Theorem 4.3 Third Angles Theorem

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…

The acute angles of a right triangle are complementary

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

Theorem 4.1 Triangle Sum Theorem

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

Theorem 4.2 Exterior Angle Theorem

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

Theorem 7

Definition of a perpendicular line

Corollary to the definition of a right…

Theorem 8

⊥ Lines form four right angles.

Two lines are perpendicular iff they form a right angle

All right angles are equal.

If the angles in a linear pair are equal, then their sides ar…

Theorem 7

⊥ Lines form four right angles.

Definition of a perpendicular line

Two lines are perpendicular iff they form a right angle

Third Angles Theorem

Side Side Side Postulate (SSS)

Side Angle Side Postulate (SAS)

Angle Side Angle Postulate (ASA)

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

When two triangles have corresponding sides equal in length,…

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

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

Third Angles Theorem

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

Side Side Side Postulate (SSS)

When two triangles have corresponding sides equal in length,…

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

Through any two points there is exactly one line.

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

If two plains intersect, then they intersect in exactly one l…

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 lines intersect, then they intersect in exactly one po…

Triangle Sum Theorem

Exterior Angle Theorem

corollary to the triangle sum theorem

Third Angle Theorem

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

The measures of an exterior angle of a triangle is equal to t…

The acute angles of a right triangle are complementary.

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

Triangle Sum Theorem

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

Exterior Angle Theorem

The measures of an exterior angle of a triangle is equal to t…

Triangle sum ... Theorem

Exterior angle theorem

Corollary to the triangle sum theorem

Third angles theorem

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…

The acute angles of a right triangle are complementary.

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

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…

Third Angles Theorem

Side Side Side Postulate (SSS)

Side Angle Side Postulate (SAS)

Angle Side Angle Postulate (ASA)

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

When two triangles have corresponding sides equal in length,…

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

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

Third Angles Theorem

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

Side Side Side Postulate (SSS)

When two triangles have corresponding sides equal in length,…

the verticle angles theorem

Alternate Interior Angles Theorem

Same-Side interior angles postulate

corresponding angles theorem

if two angles are verticle angles, than the angles are congru…

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…

the verticle angles theorem

if two angles are verticle angles, than the angles are congru…

Alternate Interior Angles Theorem

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

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.

Law of Detachment

Law of Syllogism

Properties of Congruence

Vertical Angles Theorem

If a conditional is true and its hypothesis is true, then its…

If p→q and q→r are true statements, then p→r is a true statem…

Reflexive Property: AB≅AB and ∠A≅∠A. Symmetric Property: If A…

Vertical angles are congruent.

Law of Detachment

If a conditional is true and its hypothesis is true, then its…

Law of Syllogism

If p→q and q→r are true statements, then p→r is a true statem…

Congruent Polygons

Third Angles Theorem

Side-Side-Side (SSS) Postulate

Side-Angle-Side (SAS) Postulate

Have congruent corresponding parts--their matching sides and…

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

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

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

Congruent Polygons

Have congruent corresponding parts--their matching sides and…

Third Angles Theorem

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

Pythagorean Inequalities Theorem

Triangle Sum Theorem

The acute angles of a right triangle a…

The measure of each angle of an equian…

In triangle ABC, c is the length of the longest side. If c^2…

The sum of the measures in the triangle is 180

The acute angles of a right triangle are complementary

The measure of each angle of an equiangular triangle is 60

Pythagorean Inequalities Theorem

In triangle ABC, c is the length of the longest side. If c^2…

Triangle Sum Theorem

The sum of the measures in the triangle is 180

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…

The sum of the angle measures of a tri…

The acute angles of a right triangle a…

The measure of each angle of an equian…

The measure of an exterior angle of a…

The sum of the angle measures of a triangle is ________.

The acute angles of a right triangle are ____________________…

The measure of each angle of an equiangular triangle is _____…

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

The sum of the angle measures of a tri…

The sum of the angle measures of a triangle is ________.

The acute angles of a right triangle a…

The acute angles of a right triangle are ____________________…

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…

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

SSS postulate

SAS Postulate

ASA Postulate

Isosceles triangle theorem

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

SSS postulate

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

SAS Postulate

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

Third Angles Theorem

Side-Side-Side (SSS) Postulate

Side-Angle-Side (SAS) Postulate

Angle-Side-Angle (ASA) Postulate

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

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

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

if two angles and the includes side of one triangle are congr…

Third Angles Theorem

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

Side-Side-Side (SSS) Postulate

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

SSScongruence

SAScongruence

ASAcongruence

AAScongruence

If the three sides of one triangle are respectively congruent…

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

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

If two angles and a non-included side of one triangle are res…

SSScongruence

If the three sides of one triangle are respectively congruent…

SAScongruence

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

Triangle angle Sum Theorem

Exterior Angle Theorem

Third Angles Theorem

Reflexive Property of Congruent Triang…

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…

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

For any triangle ABC, ABC is congruent to ABC

Triangle angle 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…

Third Angles Theorem

Side-side-side Postulate (SSS)

Side-angle-side Postulate (SAS)

Angle-side-angle Postulate (ASA)

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

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 a non-included side of the triangle are con…

Third Angles Theorem

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

Side-side-side Postulate (SSS)

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

Translation Postulate (Postulate 4.1)

Composition Theorem (Theorem 4.1)

If (a,b) is reflected in the x-axis...

If (a,b) is reflected in the y-axis...

a translation is a rigid motion

the composition of two (or more) rigid motion is a rigid motion

then its image is the point (a,-b)

then its image is the point (-a,b)

Translation Postulate (Postulate 4.1)

a translation is a rigid motion

Composition Theorem (Theorem 4.1)

the composition of two (or more) rigid motion is a rigid motion

Theorem 4.1: Triangle Angle-Sum Theorm

Theorem 4.2 Exterior Angle Theorem

Triangle Angle-Sum Corollaries

4.3 Third angles Theorem

The sum of the measures of the angles of a triangle is 180 ... m…

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

4.1: The acute angles of a right triangle are complementary…

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

Theorem 4.1: Triangle Angle-Sum Theorm

The sum of the measures of the angles of a triangle is 180 ... m…

Theorem 4.2 Exterior Angle Theorem

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

Corollary to a theorem

Theorem

Postulate

Triangle Sum Theorem

is a statement that can be proved easily using the theorem.

is a statement that has been proven

which is taken to be true without proof.

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

Corollary to a theorem

is a statement that can be proved easily using the theorem.

Theorem

is a statement that has been proven

SSS Postulate

SAS Postulate

ASA Postulate

Theorem 4-1

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

SSS Postulate

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

SAS Postulate

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

Postulate 5

Postulate 6

Postulate 7

Postulate 8

(1) A line contains at least two points (2) A plane contains…

Through any two points there is exactly one line.

(1) Through any three points there is at least one plane (2)…

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

Postulate 5

(1) A line contains at least two points (2) A plane contains…

Postulate 6

Through any two points there is exactly one line.

cpctc

SSS postulate

sas postulate

asa postulate

Corresponding parts of congruent triangles are congruent

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 of triangle are co…

cpctc

Corresponding parts of congruent triangles are congruent

SSS postulate

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

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, the the contrapositive of…

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

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…

If Three sides of one triangle are con…

If two sides and the included angle of…

If two angles and the included side of…

If two sides of a triangle are congrue…

Postulate 12 - SSS Postulate

Postulate 13 - SAS Postulate

Postulate 14 - ASA Postulate

Theorem 4-1: The Isosceles Triangle Theorem

If Three sides of one triangle are con…

Postulate 12 - SSS Postulate

If two sides and the included angle of…

Postulate 13 - SAS Postulate

Midpoint definition

Segment bisector definition

Congruent segments definition

Angle addition postulate

A point that divides the segment into two congruent segments

a point, line, ray, or other segment that intersects a segmen…

Segments that have the same length

Two little angles make one big angle

Midpoint definition

A point that divides the segment into two congruent segments

Segment bisector definition

a point, line, ray, or other segment that intersects a segmen…

Congruent Figures

Third Angles Theorem

SSS Postulate

SAS Postulate

Have congruent corresponding parts- their matching sides and…

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

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

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

Congruent Figures

Have congruent corresponding parts- their matching sides and…

Third Angles Theorem

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

Midpoint

Supplementary Angles

Perpendicular Lines

Congruent Angles

The point that divides, or bisects, a segment into two congru…

Two angles whose measures have the sum of 180 degrees

Two lines that intersect to form a right angle

Angles that have the same measure

Midpoint

The point that divides, or bisects, a segment into two congru…

Supplementary Angles

Two angles whose measures have the sum of 180 degrees

Theorem 4.1

Corollary 4.2

Theorem 4.3

Theorem 4.4

Each diagonal divides a parallelogram into two congruent tria…

The opposite sides and opposite angles of a parallelogram are…

Consecutive angles of a parallelogram are supplementary.

The diagonals of a parallelogram bisect each other.

Theorem 4.1

Each diagonal divides a parallelogram into two congruent tria…

Corollary 4.2

The opposite sides and opposite angles of a parallelogram are…

Parallel Lines (||)

Parallel Planes

Skew

Transversal

2 lines that never intersect

2 planes that never intersect

lines which are not coplanar and do not intersect

a line which intersects 2 or more lines

Parallel Lines (||)

2 lines that never intersect

Parallel Planes

2 planes that never intersect

Point

Line

Planes

Collinear

describe a location, no size (labeled with Capital Letters)

go on in both directions forever, infinite points on a line,…

infinite number of points contained, flat 2D, 3 points minimu…

All the points lie on same line

Point

describe a location, no size (labeled with Capital Letters)

Line

go on in both directions forever, infinite points on a line,…

AAS Theorem: 4-5-2

The Isosceles Triangle Theorem: 4-8-1

Corollary of an equiangular triangle:…

Corollary of triangle: 4-2-3

If two angles and a non-included side of one triangle are con…

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

An equilateral triangle is also equiangular.

An equilateral triangle has three 60 Degree angles

AAS Theorem: 4-5-2

If two angles and a non-included side of one triangle are con…

The Isosceles Triangle Theorem: 4-8-1

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