#### Study sets matching "geometry theorems"

#### Study sets matching "geometry theorems"

Complementary Angles

Supplementary angles

theorem

Vertical angles

Two angles whose measures equal 90 degrees

two angles whose measures equal 180 degrees

a statement that can be proven

4 angles formed by intersecting lines and facing in four diff…

Complementary Angles

Two angles whose measures equal 90 degrees

Supplementary angles

two angles whose measures equal 180 degrees

Complementary Angles

Supplementary Angles

Corresponding angles

Same side interior angles

Two angles whose measures have a sum of 90°

Two angles whose measures have a sum of 180°

Complementary Angles

Two angles whose measures have a sum of 90°

Supplementary Angles

Two angles whose measures have a sum of 180°

A-B-C-D Theorem

Theorem (Equivalence Properties of Con…

Segment Congruence Theorem

Angle Congruence Theorem

Every isometry preserves Angle measure,... Betweenness, Collinea…

For any figures F, G, and H:... 1. F=F... (Reflexive Property of Co…

Two segments are congruent if and only if they have... the same…

Two angles are congruent if and only if they have the... same me…

A-B-C-D Theorem

Every isometry preserves Angle measure,... Betweenness, Collinea…

Theorem (Equivalence Properties of Con…

For any figures F, G, and H:... 1. F=F... (Reflexive Property of Co…

A-B-C-D Theorem

Theorem (Equivalence Properties of Con…

Segment Congruence Theorem

Angle Congruence Theorem

Every isometry preserves Angle measure,... Betweenness, Collinea…

For any figures F, G, and H:... 1. F=F... (Reflexive Property of Co…

Two segments are congruent if and only if they have... the same…

Two angles are congruent if and only if they have the... same me…

A-B-C-D Theorem

Every isometry preserves Angle measure,... Betweenness, Collinea…

Theorem (Equivalence Properties of Con…

For any figures F, G, and H:... 1. F=F... (Reflexive Property of Co…

Vertical Angles Theorem

Straight Angles Theorem

Corresponding Angles Theorem

Alternate Interior Angles Theorem

"Vertical Angles are Congruent"

"Straight angles sum to 180 degrees"

"If lines parallel, then corresponding angles congruent"

"If lines parallel, then alternate interior angles congruent"

Vertical Angles Theorem

"Vertical Angles are Congruent"

Straight Angles Theorem

"Straight angles sum to 180 degrees"

Two lines perpendicular to the same li…

Opposite sides of a parallelogram are…

Opposite angles of a parallelogram are…

Diagonals of a parallelogram bisect ea…

Why is this true?

Why is this true?

Why is this true?

Two lines perpendicular to the same li…

Opposite sides of a parallelogram are…

Why is this true?

linear pair theorem

congruent supplements theorem

right angle congruence theorem

congruent complements theorem

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

if two angles are supplementary to the same angle (or two con…

all right angles are congruent

if two angles are complementary to the same angle ( or two co…

linear pair theorem

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

congruent supplements theorem

if two angles are supplementary to the same angle (or two con…

Exterior angle theorem

Exterior angle sum theorem

Vertical angle theorem

Triangle inequality theorem

An exterior angle of a triangle is greater than either remote…

The measure of exterior < equals the measurement of the remot…

If two angles are vertical <'s then they are equal

In any given triangle, the sum of any two sides of the triang…

Exterior angle theorem

An exterior angle of a triangle is greater than either remote…

Exterior angle sum theorem

The measure of exterior < equals the measurement of the remot…

Theorem 3-9

Theorem 3-10

Theorem 3-11

Postulate 3-2

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

if two lines are perpendicular to the same line, then they ar…

if a line is perpendicular to one of two parallel lines, then…

if two lines and a transversal form corresponding angles that…

Theorem 3-9

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

Theorem 3-10

if two lines are perpendicular to the same line, then they ar…

Vertical Angle Theorem

Isosceles Trapezoid Theorem

Linear Pair Theorem

Corresponding Parts of Congruent Trian…

If two non-consecutive angles are congruent, then they are ve…

If a quadrilateral is an Isosceles Trapezoid, then it has con…

If two angles sharing one ray and endpoint measure 180, then…

The corresponding parts of congruent triangles are congruent.

Vertical Angle Theorem

If two non-consecutive angles are congruent, then they are ve…

Isosceles Trapezoid Theorem

If a quadrilateral is an Isosceles Trapezoid, then it has con…

Postualte 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

Through any two points there is exactly one line

If two lines intersect, they intersect in exactly one point

If two planes intersect, then they intersect in a line

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

Postualte 1-1

Through any two points there is exactly one line

Postulate 1-2

If two lines intersect, they intersect in exactly one point

right angles congruence theorem

congruent supplements theorem

vertical angles congruence theorem

corresponding angles theorem

all right angles are congruent

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

vertical angles are congruent

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

right angles congruence theorem

all right angles are congruent

congruent supplements theorem

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

Vertical angles theorem

Congruent supplements theorem

Congruent complements theorem

Theorem 2-5

Vertical angles are congruent

If two angles are supplements of the same angle (or of congru…

If two angles are complements of the same angle (or of congru…

If two angles are congruent and supplementary, then each is a…

Vertical angles theorem

Vertical angles are congruent

Congruent supplements theorem

If two angles are supplements of the same angle (or of congru…

theorem

Vertical angles

Angle addition Postulate

Linear pair theorem

a statement that can be proven

4 angles formed by intersecting lines and facing in four diff…

for any angle, the measure of the whole is equal to the sum o…

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

theorem

a statement that can be proven

Vertical angles

4 angles formed by intersecting lines and facing in four diff…

Theorem 2-4

Theorem 2-5

Theorem 2-6

Theorem 2-1

If two lines are perpendicular, then they form congruent adja…

If two lines form congruent adjacent angles, then two lines a…

If the exterior sides of two adjacent acute angles are perpen…

If M is the midpoint of AB, then AM equals 1/2 ab and MB equa…

Theorem 2-4

If two lines are perpendicular, then they form congruent adja…

Theorem 2-5

If two lines form congruent adjacent angles, then two lines a…

Vertical angles theorem

Congreunt 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 two angl…

If two angles are complements of the same angle then two angl…

If two angles are right then they are congruent

Vertical angles theorem

If two angles are vertical then they are congruent

Congreunt supplements theorem

If two angles are supplements of the same angle then two angl…

Vertical angles therom

Segment addition postulate

Law of detachment

Law of syllogism

IF two angles are vertical angles, thewn they are congruent.

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

If P->Q is a true statement and P is true, then Q is true

Is p ->Q and Q ->r are true statements, then p ->r is a true…

Vertical angles therom

IF two angles are vertical angles, thewn they are congruent.

Segment addition postulate

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

Congruent segments

Midpoint

Segment bisector

Congruent angles

If two segments are congruent, then they have equal measure

If a point is a midpoint, then it divides a segment into two…

If a point, line, Ray, or segment is a segment bisector, then…

If two angles are congruent then they have equal measure

Congruent segments

If two segments are congruent, then they have equal measure

Midpoint

If a point is a midpoint, then it divides a segment into two…

vertical angles theorem

alternate interior angles theorem

congruent complement theorem

same side interior angles theorem

vertical angles are congruent

alternate interior angles are congruent

g

same side interior angles are supplementary

vertical angles theorem

vertical angles are congruent

alternate interior angles theorem

alternate interior angles are congruent

congruent supplements theorem

congruent complements theorem

VAT

3.1

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

if two lines intersect to form a linear pair of congruent ang…

congruent supplements theorem

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

congruent complements theorem

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

2.1 - the midpoint theorem

2.2

2.3 - the supplement theorem

2.4 - complement theorem

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

Congruence of segments is reflexive, symmetric, and transitive

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

If 2 adjacent angles form a right angle, then they are comple…

2.1 - the midpoint theorem

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

2.2

Congruence of segments is reflexive, symmetric, and transitive

Properties of Segment Congruence

Properties of Angle Congruence

Right Angles Congruence Theorem

Congruent Supplements Theorem

Segment congruence is reflexive, symmetric, and transitive.

Angle congruence is reflexive, symmetric, and transitive.

All right angles are congruent.

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

Properties of Segment Congruence

Segment congruence is reflexive, symmetric, and transitive.

Properties of Angle Congruence

Angle congruence is reflexive, symmetric, and transitive.

Addition Prop of Equality

Subtraction Prop of Equality

Multiplication Prop of Equality

Division Prop 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 does not equal 0, then a divided by c = b divi…

Addition Prop of Equality

If a = b, then a + c = b + c

Subtraction Prop of Equality

If a = b, then a - c = b - c

Theorem 2.1... (Properties of Segment Con…

Theorem 2.2... (Properties of Angle Congr…

Right Angles Congruence Theorem (Theor…

Congruent Supplements Theorem ... (Theore…

Segment congruence is reflexive, symmetric, and transitive... Re…

Angle congruence is reflexive, symmetric, and transitive... Refl…

All right angles are congruent.

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

Theorem 2.1... (Properties of Segment Con…

Segment congruence is reflexive, symmetric, and transitive... Re…

Theorem 2.2... (Properties of Angle Congr…

Angle congruence is reflexive, symmetric, and transitive... Refl…

Linear Pair Theorem

Segment/Angle Addition Theorem

Segment/Angle Subtraction Theorem

Reflexive Theorem

If two angles are a linear pair then they are supplementary

If a segment/angle is added to congruent segments/angles then…

If a segment/angle is subtracted from congruent segments/angl…

If there is an object, then it is congruent to itself

Linear Pair Theorem

If two angles are a linear pair then they are supplementary

Segment/Angle Addition Theorem

If a segment/angle is added to congruent segments/angles then…

Polygon

Linear pair theorem

Congruent supplements theorem

Angle addition postulate

A closed plane figure with 3 or more libe segments that inste…

If two angles form a linear pair they are supplementary

If two angles are supplementary to two angles then the two an…

Adding two angles together creates a new angle that's measure…

Polygon

A closed plane figure with 3 or more libe segments that inste…

Linear pair theorem

If two angles form a linear pair they are supplementary

Perpendicular Bisector Theorem

Converse of the Perpendicular Bisector…

Angle Bisector Theorem

Converse of the Angle Bisector Theorem

In a plane, if a point lies on the perpendicular bisector of…

In a plane, if a point is equidistant from the endpoints of a…

If a point lies on the bisector of an angle, then it is ... equi…

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

Perpendicular Bisector Theorem

In a plane, if a point lies on the perpendicular bisector of…

Converse of the Perpendicular Bisector…

In a plane, if a point is equidistant from the endpoints of a…

Definition of complementary angles

Definition of supplementary angles

Equal angle measures theorem

Definition of linear pair

If the measures of two angles are r and s, then the angles ar…

If the measures if two angles are r and a, then the angles ar…

If two angles have the same measure, their complements have t…

Two adjacent angles are a linear pair of and only if their no…

Definition of complementary angles

If the measures of two angles are r and s, then the angles ar…

Definition of supplementary angles

If the measures if two angles are r and a, then the angles ar…

Theorem 4

Theorem 5

Theorem 6

Theorem 7

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

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

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

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

Theorem 4

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

Theorem 5

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

Midpoint Theorem

Point Theorem

Supplement Theorem

Vertical Angle Theorem

If P is the midpoint of TF, then PF = 1/2 TF

On any line L, there are 5 different points on L

Supplements of congruent angles are congruent

Vertical angles are congruent

Midpoint Theorem

If P is the midpoint of TF, then PF = 1/2 TF

Point Theorem

On any line L, there are 5 different points on L

The sum of the lengths of any two side…

The perpendicular segment from a point…

Two sides of a triangle are congruent…

If two sides of a triangle are congrue…

Theorem 5.11

Theorem 5.12

Theorem 5.13

Theorem 5.14

The sum of the lengths of any two side…

Theorem 5.11

The perpendicular segment from a point…

Theorem 5.12

3-1: parallel plane intersect theorem

3-2: alternate interior angle theorem

3-3: same side interior angles theorem

3-4: perpendicular transversal theorem

if two parallel planes are cut by a third plane, then the int…

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

if two parallel lines are cut by a transversal, then same-sid…

if a transversal perpendicular to one of two parallel lines,…

3-1: parallel plane intersect theorem

if two parallel planes are cut by a third plane, then the int…

3-2: alternate interior angle theorem

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

Perpendicular lines

Parallel lines

Midpoint of a segment

Triangle Area/Perimeter Formulas

2 lines are perpendicular if-f their slope product is 1

2 lines are parallel if-f they have the same slope

If midpoint => 2 = segments

P=a+b+c, A=1/2 bh

Perpendicular lines

2 lines are perpendicular if-f their slope product is 1

Parallel lines

2 lines are parallel if-f they have the same slope

Theorem 6.1

Theorem 6.2

Theorem 6.3

Theorem 6.4

Congruent Segment Bisector Theorem: If two segments are bisec…

Segment Congruence is an equivalent relation

Supplements of congruent angles are congruent

Compliments of congruent angles are congruent

Theorem 6.1

Congruent Segment Bisector Theorem: If two segments are bisec…

Theorem 6.2

Segment Congruence is an equivalent relation

angle bisector

Complementary Angles

Supplementary angles

theorem

a ray that begins at the vertex of an angle and divides the a…

Two angles whose measures equal 90 degrees

two angles whose measures equal 180 degrees

a statement that can be proven

angle bisector

a ray that begins at the vertex of an angle and divides the a…

Complementary Angles

Two angles whose measures equal 90 degrees

Theorem 5

Theorem 6

Theorem 7

Theorem 8

if a triangle has equal sides then the corresponding angles a…

equal angles in a triangle mean that the corresponding sides…

S.S.S.

If a point l is not on line x only one line is perpendicular…

Theorem 5

if a triangle has equal sides then the corresponding angles a…

Theorem 6

equal angles in a triangle mean that the corresponding sides…

Pythagorean Theorem

Linear Pair Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

In a right triangle, the sum of squares of the lengths of the…

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

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

If two angles are complementary to the same angle(or to two c…

Pythagorean Theorem

In a right triangle, the sum of squares of the lengths of the…

Linear Pair Theorem

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

Theorem 3.8

Theorem 3.9

Theorem 3.10

Theorem 3.11

If two lines intersect to form a linear pair of congruent ang…

If two lines are perpendicular, then they intersect to form f…

If two sides of two adjacent angles are perpendicular, then t…

If a transversal is perpendicular to one of the other paralle…

Theorem 3.8

If two lines intersect to form a linear pair of congruent ang…

Theorem 3.9

If two lines are perpendicular, then they intersect to form f…

Vertical Angles Theorem (2-1):

Congruent Supplements Theorem (2-2):

Congruent Complements Theorem (2-3):

Theorem 2-4:

Vertical Angles are congruent.

If two angles are supplements of the same angle (or of congru…

If two angles are complements of the same angle (or of congru…

All right angles are congruent.

Vertical Angles Theorem (2-1):

Vertical Angles are congruent.

Congruent Supplements Theorem (2-2):

If two angles are supplements of the same angle (or of congru…

Theorem 2-4

Theorem 2-5

Theorem 2-6

Theorem 2-7

If two lines are perpendicular, then they form congruent adja…

If two lines form congruent adjacent angles, then the lines a…

If the exterior sides of two adjacent acute angles are perpen…

If two angles are supplements of congruent angles (or of the…

Theorem 2-4

If two lines are perpendicular, then they form congruent adja…

Theorem 2-5

If two lines form congruent adjacent angles, then the lines a…

Reflexive Property of Segment Conguence

Symmetric Property of Segment Congruence

Transitive Property of Segment Congrue…

Reflexive Property of Angle Congruence

For any segment AB, seg AB≅seg AB

If seg AB≅seg CD, then seg CD≅seg AB

If seg AB≅seg CD and seg CD≅ seg EF, then seg AB≅seg EF

For any angle A, <A≅<A

Reflexive Property of Segment Conguence

For any segment AB, seg AB≅seg AB

Symmetric Property of Segment Congruence

If seg AB≅seg CD, then seg CD≅seg AB

Triangle angle sum theorem

Exterior angle theorem

Isosceles triangle theorem

Converse isosceles triangle theorem

The measures of the angles in a triangle add up to 180 degrees.

The measure of an exterior angle is equal to the sum of its r…

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

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

Triangle angle sum theorem

The measures of the angles in a triangle add up to 180 degrees.

Exterior angle theorem

The measure of an exterior angle is equal to the sum of its r…

Vertical angles

Linear pairs

Adjacent angles

Corresponding angles

All vertical angles are congruent

Linear pairs form supplementary angles

Consecutive adjacent angles are supplementary

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

Vertical angles

All vertical angles are congruent

Linear pairs

Linear pairs form supplementary angles

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