#### Study sets matching "geometry chapter 4 theorems postulates"

#### Study sets matching "geometry chapter 4 theorems postulates"

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…

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…

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…

Triange Sum Theorem

Corollary 4-2-2

Corollary 4-2-3

Exterior Angle Theorem

The sum of the angle measues of a triangle is 180 degrees.

The acute angles of a right triangle are complementary.

The measures of each angle of an equiangular triangle is 60 d…

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

Triange Sum Theorem

The sum of the angle measues of a triangle is 180 degrees.

Corollary 4-2-2

The acute angles of a right triangle are complementary.

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…

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…

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 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…

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

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 ____________________…

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

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…

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…

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,…

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…

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…

Triangle Angle-Sum Theorem

Exterior Angle Theorem

Third Angles Theorem

Side Side Side Congruence

The sum of the measures of the angles of a triangle is 180

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…

If three sides of one triangle are congruent to these three s…

Triangle Angle-Sum Theorem

The sum of the measures of the angles of a triangle is 180

Exterior Angle Theorem

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

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

Translation Postulate

Composition Theorem

Reflection Postulate

Rotation Postulate

A translation is a rigid motion.

The composition of two (or more) rigid motions is a rigid mot…

A reflection is a rigid motion.

A rotation is a rigid motion.

Translation Postulate

A translation is a rigid motion.

Composition Theorem

The composition of two (or more) rigid motions is a rigid mot…

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

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…

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…

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…

Law Of Detachment

Law of Syllogism

Vertical Angle Theorem (VAT)

Reflexive Property

An argument in the form of "P=>Q", or "If P then Q"

Relates several different arguments and uses the form ... If P=>…

Vertical angles are congruent

A=A

Law Of Detachment

An argument in the form of "P=>Q", or "If P then Q"

Law of Syllogism

Relates several different arguments and uses the form ... If P=>…

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…

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…

Reflexive Property

Symmetric Property

Transitive Property

Add/Subtract Property

For every number a, a = a.

For all numbers a & b, if a = b, then b = a.(ex. the segment…

For all numbers a, b & c, if a = b & b = c, then a = c. (A bi…

For all numbers a, b, & c, if a = b, then a + c = b + c and a…

Reflexive Property

For every number a, a = a.

Symmetric Property

For all numbers a & b, if a = b, then b = a.(ex. the segment…

Congruent Figures

Third Angles Theorem

Angle-Side-Angle Postulate

Hypotenuse-Leg Theorem

figures of the same size shape and length

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

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

This theorem states that 'if the hypotenuse and one leg of a…

Congruent Figures

figures of the same size shape and length

Third Angles Theorem

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

Triangle Sum Theorem

The acute angles of a right triangle a…

The measure of each angle of an equian…

Exterior Angle Theorem

The sum of the angle measures of a triangle is 180 degrees.

...

...

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

Triangle Sum Theorem

The sum of the angle measures of a triangle is 180 degrees.

The acute angles of a right triangle a…

...

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

Law Of Detachment

Law of Syllogism

Vertical Angle Theorem (VAT)

Reflexive Property

An argument in the form of "P=>Q", or "If P then Q"

Relates several different arguments and uses the form ... If P=>…

Vertical angles are congruent

A=A

Law Of Detachment

An argument in the form of "P=>Q", or "If P then Q"

Law of Syllogism

Relates several different arguments and uses the form ... If P=>…

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…

Reflexive property

Symmetric propetry

Transitive property

Definition of Midpoint

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

Point on that line segment that divides the segment two congr…

Reflexive property

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

Symmetric propetry

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

Triangle Sum Theorem

Exterior Angle Theorem

Third Angles Theorem

SAS Congruence 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…

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

If two sides and the included angle are congruent to two side…

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…

If a triangle has at least two congrue…

If a triangle has at least two congrue…

Each angle of an equilateral triangle is

Equilateral triangles are

Isosceles Triangle Theorem (ITT)

ITT Converse

60 degrees

equiangular

If a triangle has at least two congrue…

Isosceles Triangle Theorem (ITT)

If a triangle has at least two congrue…

ITT Converse

scalene

isosceles

equilateral

acute triangle

triangle with no side congruent

triangle with at least two sides congruent

triangle with all sides congruent

all angle measures less than 90

scalene

triangle with no side congruent

isosceles

triangle with at least two sides congruent

Triangle Sum Theorem

Exterior Angle Theorem

Corollary to 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…

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

SSS postulate

SAS Postulate

ASA postulate

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

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

If two sides and the included angle of one triangle is congru…

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

Theorem 4-1

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

SSS postulate

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

Law Of Detachment

Law of Syllogism

Vertical Angle Theorem (VAT)

Reflexive Property

An argument in the form of "P=>Q", or "If P then Q"

Relates several different arguments and uses the form ... If P=>…

Vertical angles are congruent

A=A

Law Of Detachment

An argument in the form of "P=>Q", or "If P then Q"

Law of Syllogism

Relates several different arguments and uses the form ... If P=>…

SSS Postulate (side side side)

SAS Postulate (side angle side)

ASA Postulate (angle side angle)

ITT (Isosceles Triangle Theorem)

If 3 sides of one triangle are congruent to 3 sides of anothe…

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 (side side side)

If 3 sides of one triangle are congruent to 3 sides of anothe…

SAS Postulate (side angle side)

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