Study sets matching "geo geometry theorems"

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Study sets matching "geo geometry theorems"

41 terms
Geometry theorems
Linear Pair Theorem
Vertical Angles Theorem
Corresponding Angles Postulate
Two Perps Theorem
If two angles form a linear pair, then they are supplementary.
If two angles are vertical angles, then they are congruent.
If two parallel lines are cut by a transversal, then the pair…
If two lines are perpendicular to the same line, then the lin…
Linear Pair Theorem
If two angles form a linear pair, then they are supplementary.
Vertical Angles Theorem
If two angles are vertical angles, then they are congruent.
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
37 terms
Geometry Theorems
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.
37 terms
Geometry Theorems
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.
14 terms
Geometry Theorems
Corresponding Angles Theorem
Alternate Interior Angles Theorem
Alternate Exterior Angles Theorem
Same-Side Interior Angles Theorem
If two lines are parallel and intersected by a transversal, t…
If two lines are parallel and intersected by a transversal, t…
If two lines are parallel and intersected by a transversal, t…
If two lines are parallel and intersected by a transversal, t…
Corresponding Angles Theorem
If two lines are parallel and intersected by a transversal, t…
Alternate Interior Angles Theorem
If two lines are parallel and intersected by a transversal, t…
26 terms
geometry theorems
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…
58 terms
Geometry: Theorems
Theorem 1-1
Theorem 1-2
Theorem 1-3
Midpoint Theorem
If two lines intersect, then they intersect exactly in one po…
Through a line and a point not on the line there is exactly o…
If two lines intersect, then exactly one plane contains the l…
If M is the midpoint of AB, then AM = 1/2 AB and MB = 1/2 AB.
Theorem 1-1
If two lines intersect, then they intersect exactly in one po…
Theorem 1-2
Through a line and a point not on the line there is exactly o…
Geometry-Theorems
Congruent Supplements Theorem
Congruent Complements Theorem
Vertical Angles Congruence Theorem
Congruence of Segments Theorem
If two angles are supplementary the to the same angle, then t…
If two angles are complementary to the same angle, then the t…
If two angles are vertical angles, then they are congruent.
Segment congruence is reflexive, symmetric, and transitive.
Congruent Supplements Theorem
If two angles are supplementary the to the same angle, then t…
Congruent Complements Theorem
If two angles are complementary to the same angle, then the t…
33 terms
Geometry Theorems
Corresponding Angles Postulate
Corresponding Angles Converse
Alternate Interior Angles
Alternate Exterior Angles
p: 2 parallel lines are cut by a transversal ... q: pairs of cor…
p: 2 lines are cut by a transversal and corresponding angles…
p: 2 parallel lines are cut by a transversal ... q: alternate in…
p: 2 parallel lines are cut by a transversal ... q: alternate ex…
Corresponding Angles Postulate
p: 2 parallel lines are cut by a transversal ... q: pairs of cor…
Corresponding Angles Converse
p: 2 lines are cut by a transversal and corresponding angles…
Geometry Theorems
Corresponding Angles Postulate
Converse
Converse of Corresponding Angles Postu…
Vertical Angle Theorem
If lines a parallel than corresponding angles are congruent
A converse swapd the hypothesis and conclusion
If- Corresponding angles are congruent... Then- The lines are pa…
If two angles are vertical then they are congruent
Corresponding Angles Postulate
If lines a parallel than corresponding angles are congruent
Converse
A converse swapd the hypothesis and conclusion
18 terms
Geometry Theorems
Theorem 1
Theorem 2
Segment Bisector Colinear
Converse, Inverse, Contrapositive
If two right angles are right angles, then they are congruent
If two angles are straight angles, then they are congruent
If a point(etc.) divides a segment into two congruent segment…
T Given BPS --> AG... F Converse AG --> BPS... F Inverse ~BPS --> ~…
Theorem 1
If two right angles are right angles, then they are congruent
Theorem 2
If two angles are straight angles, then they are congruent
Geometry Theorems
Distance formula
Midpoint formula
Slope formula
Slope intercept formula
Distance formula
Midpoint formula
Geometry Theorems
Theorem 2.1: Congruence of Segments
Theorem
Theorem 2.2: Congruence of Angles
Theorem 2.3: Right Angles Congruence T…
Segment congruence is reflexive, symmetric, and transitive
a statement that can be proven
Angle congruence is reflexive, symmetric, and transitive
All right angles are congruent
Theorem 2.1: Congruence of Segments
Segment congruence is reflexive, symmetric, and transitive
Theorem
a statement that can be proven
15 terms
Geometry Theorems
Theorem 2.2 "Congruent Supplements The…
Theorem 2.3 "Congruent Complementary T…
Theorem 2.4 "No Name"
Theorem 2.5 "No Name"
IF angle 1 and angle 3 are supplementary and angle 2 and angl…
IF angle 1 and angle 2 are complementary and angle 2 and angl…
All right angle are congruent
IF two angles are congruent and supplementary... THEN each angle…
Theorem 2.2 "Congruent Supplements The…
IF angle 1 and angle 3 are supplementary and angle 2 and angl…
Theorem 2.3 "Congruent Complementary T…
IF angle 1 and angle 2 are complementary and angle 2 and angl…
18 terms
Geometry Theorems
Theorem 2.1 - Congruence of Segments
Theorem 2.2 - Congruence of Angles
Theorem 2.3 - Right Angles Congruence…
Theorem 2.4 - Congruent Supplements Th…
Segment congruence is reflexive, symmetric, transitive.... Ref…
Angle congruence is reflexive, symmetric, and transitive.... R…
All right angles are congruenet
If two angles are supplements of the same angle (or to congru…
Theorem 2.1 - Congruence of Segments
Segment congruence is reflexive, symmetric, transitive.... Ref…
Theorem 2.2 - Congruence of Angles
Angle congruence is reflexive, symmetric, and transitive.... R…
48 terms
Geometry Theorems
The Reflexive Property
The Symmetric Property
The Transitive Property
The Substitution Postulate
a=a
If a=b, then b=a
If a=b and b=c, then a=c
If a=b and b+c=d, then a+c=d
The Reflexive Property
a=a
The Symmetric Property
If a=b, then b=a
37 terms
Geometry Theorems
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.
14 terms
Geometry Theorems
Theorem 5.1- Midsegment Theorem
Theorem 5.2- Perpendicular bisector Th…
Theorem 5.3- Converse of the Perpendic…
Theorem 5.4- Concurrency of Perpendicu…
The segment connecting the midpoints of two sides of a triang…
In a plane, if a point is equidistant from the endpoints of a…
In a plane, if a point is equidistant from the endpoints of a…
The perpendicular bisectors of a triangle intersect at a poin…
Theorem 5.1- Midsegment Theorem
The segment connecting the midpoints of two sides of a triang…
Theorem 5.2- Perpendicular bisector Th…
In a plane, if a point is equidistant from the endpoints of a…
14 terms
Geometry Theorems
Definition of perpendicular
definition of complementary
definition of supplementary
Reflexive property
lines meet at right angles
two or more angels add to 90 degrees
two or more angels add to 180 degrees
any segment is congruent to itself
Definition of perpendicular
lines meet at right angles
definition of complementary
two or more angels add to 90 degrees
25 terms
Geometry Theorems
Linear Pair Theorem
Congruent Supplement Theorem
Congruent Complement Theorem
Reflexive Theorem
If two angles are a linear pair, then they are supplementary
Supplements of congruent angles are congruent to each other
Complements of congruent angles are congruent to each other
Every object is congruent to itself
Linear Pair Theorem
If two angles are a linear pair, then they are supplementary
Congruent Supplement Theorem
Supplements of congruent angles are congruent to each other
19 terms
Geometry Theorems
Linear Pair Theorem
Congruent Supplements Theorem
Reflexive Theorem
Segment and Angle Addition
If they are linear pairs then they are always supplementary.
If there are supplements or congruent angles, then they are c…
Every object is congruent to itself.
If a segment of angle is added to congruent segments the resu…
Linear Pair Theorem
If they are linear pairs then they are always supplementary.
Congruent Supplements Theorem
If there are supplements or congruent angles, then they are c…
10 terms
geometry theorems
Perpendicular conditional
Perpendicular converse
Complementary conditional
Complementary converse
if 2 lines are perpendicular then they form a right angle
if 2 lines intersect at a right angle then they are perpendic…
if 2 angles are comp. then they form a right angle
if 2 angles from a right angle then they are comp.
Perpendicular conditional
if 2 lines are perpendicular then they form a right angle
Perpendicular converse
if 2 lines intersect at a right angle then they are perpendic…
Geometry Theorems
If two angles form a vertical angle, t…
If two angles are supplements of the s…
If two angles are complements of the s…
All right angles are congruent
vertical angles
congruent Supplements
congruent Complements
right angles
If two angles form a vertical angle, t…
vertical angles
If two angles are supplements of the s…
congruent Supplements
63 terms
Geometry theorems
Linear Pair theorem
Congruent Supplements Theorem
Congruent Complements Theorem
Reflexive Theorem
Two linear pair angles that are always supplementary.
Supplements of congruent angles are congruent to each other
Complements of congruent angles are congruent to eachother
every object is congruent to itself. (like a mirror) (used wi…
Linear Pair theorem
Two linear pair angles that are always supplementary.
Congruent Supplements Theorem
Supplements of congruent angles are congruent to each other
12 terms
Geometry Theorems
Jeff Corresponding angles Postulate
Alternate interior angles theorem
Alternate exterior angles theorem
Consecutive interior angles theorem
When two parallel lines are cut by a traversal, the resulting…
When two parallel lines are cut by a transversal.
If two parallel lines are cut by a transversal, then the alte…
When two lines are cut by a transversal, the pair of angles o…
Jeff Corresponding angles Postulate
When two parallel lines are cut by a traversal, the resulting…
Alternate interior angles theorem
When two parallel lines are cut by a transversal.
82 terms
Geometry Theorems
If a-b > 0, then
If a=b+c, and c>0, then
Let A, B, and C be points of a line, w…
If A, B, and C are three different poi…
a>b
a>b
A-B-C
Exactly one of them is between the other two
If a-b > 0, then
a>b
If a=b+c, and c>0, then
a>b
9 terms
Geometry Theorems
Angle-Side Theorem
Two equidistant points
Point on perpendicular bisector... (Equid…
Four Ways to Determine a Plane
If two angles of a triangle are congruent, the sides opposite…
Two points each equidistant from the endpoints of a segment d…
A point on the perpendicular bisector is equidistant from the…
1. Three noncollinear points determine a plane... 2. A line and…
Angle-Side Theorem
If two angles of a triangle are congruent, the sides opposite…
Two equidistant points
Two points each equidistant from the endpoints of a segment d…
16 terms
Geometry Theorems
Properties of Segment Congruence
Properties of Angles Congruence
Right Angles Congruence Theorem
Congruent Supplements Theorem
This theorem is reflective, symmetric, and transitive.
Angle congruence is reflective, symmetric, and transitive.
All right angles are congruent.
If two angles are supplementary to the same angle (or to cong…
Properties of Segment Congruence
This theorem is reflective, symmetric, and transitive.
Properties of Angles Congruence
Angle congruence is reflective, symmetric, and transitive.
Geometry Theorems
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
If the same number is added to equal ... numbers, then the sums…
If the same number is subtracted from equal ... numbers, then th…
If equal numbers are multiplied by the same ... number, then the…
If equal numbers are divided by the same ... number, then the qu…
Addition Property of Equality
If the same number is added to equal ... numbers, then the sums…
Subtraction Property of Equality
If the same number is subtracted from equal ... numbers, then th…
64 terms
Geometry Postulates and Theorems
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
GEOMETRY: THEOREMS
Problem : In what kind of triangle is…
Problem : In what kind of triangle is…
Problem : What does it say about a tri…
Problem : What must be true of a trian…
An equilateral triangle
An equilateral triangle
The triangle is a right triangle.
The triangle must be acute.
Problem : In what kind of triangle is…
An equilateral triangle
Problem : In what kind of triangle is…
An equilateral triangle
Geometry Definitions, Postulates and Theorems
Complementary angles
Supplementary angles
Theorem
Vertical Angles
two angles whose measures have a sum of 90°
two angles who measures have a sum of 180°
a statement that can be proven
two angles formed by intersecting lines and facing in the opp…
Complementary angles
two angles whose measures have a sum of 90°
Supplementary angles
two angles who measures have a sum of 180°
58 terms
Geometry: Theorems
Theorem 1-1
Theorem 1-2
Theorem 1-3
Midpoint Theorem
If two lines intersect, then they intersect exactly in one po…
Through a line and a point not on the line there is exactly o…
If two lines intersect, then exactly one plane contains the l…
If M is the midpoint of AB, then AM = 1/2 AB and MB = 1/2 AB.
Theorem 1-1
If two lines intersect, then they intersect exactly in one po…
Theorem 1-2
Through a line and a point not on the line there is exactly o…
Geometry Theorems
Properties of Segment Congruence... (Refl…
Properties of Angles Congruence... (Refle…
Right Angles Congruence Theorem
Congruent Supplements Theorem
Reflexive: For any segment AB, segment AB is congruent to seg…
Reflexive: For any angle A, angle A is congruent to angle A... S…
All right angles are congruent
If two angles are supplementary to the same angle (or to cong…
Properties of Segment Congruence... (Refl…
Reflexive: For any segment AB, segment AB is congruent to seg…
Properties of Angles Congruence... (Refle…
Reflexive: For any angle A, angle A is congruent to angle A... S…
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
16 terms
Geometry Theorems
Same side interior angles postulate
Alternate Interior angles theorem
Perpendicular Transversal Theorem
Corollary to the corresponding angles…
If two parallel lines are cut by a transversal, then the pair…
If 2 parallel lines are cut by a transversal, then the pairs…
If a transversal is perpendicular to a parallel line, then it…
If 2 coplanar lines are perpendicular to the same line, then…
Same side interior angles postulate
If two parallel lines are cut by a transversal, then the pair…
Alternate Interior angles theorem
If 2 parallel lines are cut by a transversal, then the pairs…
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
48 terms
Geometry Theorems
MULTIPLICATION THEOREM OF CONGRUENCE
DIVISION THEOREM OF CONGRUENCE
If two angles are right angles, then t…
If two angles are complementary to the…
If congruent segments/angles are multiplied by a constant, th…
If congruent segments/angles are divided by a non-zero consta…
...
...
MULTIPLICATION THEOREM OF CONGRUENCE
If congruent segments/angles are multiplied by a constant, th…
DIVISION THEOREM OF CONGRUENCE
If congruent segments/angles are divided by a non-zero consta…
Geometry-Theorems
Congruent Supplements Theorem
Congruent Complements Theorem
Vertical Angles Theorem
Congruence of Segments Theorem
If two angles are supplementary the to the same angle, then t…
If two angles are complementary to the same angle, then the t…
If two angles are vertical angles, then they are congruent.
Segment congruence is reflexive, symmetric, and transitive.
Congruent Supplements Theorem
If two angles are supplementary the to the same angle, then t…
Congruent Complements Theorem
If two angles are complementary to the same angle, then the t…
50 terms
Geometry Theorems
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
Pythagorean Theorem
If B is between A and C, then AB+BC=AC.
Given segment AB and a point O on segment AB, all rays that c…
If S is in the interior of angle PQR, then measure angle PQS…
In a right triangle, the sum of the squares of the lengths of…
Segment Addition Postulate
If B is between A and C, then AB+BC=AC.
Protractor Postulate
Given segment AB and a point O on segment AB, all rays that c…
16 terms
Geometry Theorems
Congruent Supplementaries
Congruent Compliments
Congruent Right Angles
Congruent and Supplementary Angles
If two angles are supplements of the same angle then they are…
If two angles are compliments of the same angle then they are…
All right angles are congruent
If two angles are congruent and supplementary then they are b…
Congruent Supplementaries
If two angles are supplements of the same angle then they are…
Congruent Compliments
If two angles are compliments of the same angle then they are…
20 terms
Geometry Theorems
Theorem 1
Theorem 1a
Theorem 2
Theorem 2a
If 2 angles are equal then their supplements are equal
If 2 supplements are equal then the angles are equal
If 2 angles are equal then their complements are equal
If 2 complements are equal them the angles are equal
Theorem 1
If 2 angles are equal then their supplements are equal
Theorem 1a
If 2 supplements are equal then the angles are equal
6 terms
Geometry Theorems
ASA
SAS
HL
NEI
-angle ... -side ... -angle
-side ... -angle ... -side
-hypotenuse ... -leg
-not ... -enough ... -info
ASA
-angle ... -side ... -angle
SAS
-side ... -angle ... -side
64 terms
Geometry Postulates and Theorems
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
6 terms
Geometry Theorems
Theorem
Vertical Angles Theorem (2-1)
Congruent Supplements Theorem (2-2)
Congruent Complements Theorem (2-3)
a statement that you prove or that is proven to be true
vertical angles are congruent
if 2 angles are supplements of the same angle or of congruent…
if 2 angles are complements of the same angle or of congruent…
Theorem
a statement that you prove or that is proven to be true
Vertical Angles Theorem (2-1)
vertical angles are congruent
21 terms
Geometry Theorems
The Pythagorean Theorem
The Triangle Angle Sum Theorem
Theorem 3
Theorem 4
The square of the hypotenuse of a right triangle is equal to…
The sum of the angles of a triangle is 180 degrees
If the diameter of a circle is d, it's circumference is Pi d
If the radius of a circle is r, its area is Pi r squared
The Pythagorean Theorem
The square of the hypotenuse of a right triangle is equal to…
The Triangle Angle Sum Theorem
The sum of the angles of a triangle is 180 degrees
7 terms
Geometry theorems
Congruences of segments
Congruence of angles
Right angles congruence theorem
Congruent supplements theorem
Segement congruence is reflexive, symmetric, transitive
Angle congruence is reflexive, symmetric, transitive
All right angles are congruent
If two angles are supplementary to the same angle, then they…
Congruences of segments
Segement congruence is reflexive, symmetric, transitive
Congruence of angles
Angle congruence is reflexive, symmetric, transitive
Geometry Theorems
Vertical Angles Theorem
Congruent Supplements Theorem
Congruent Complements Theorem
Theorem 2-4
Vertical angles are congruent
If 2 angles are supplements of the same angle (or congruent a…
If 2 angles are complements of the same angle (of congruent a…
All right angles are congruent.
Vertical Angles Theorem
Vertical angles are congruent
Congruent Supplements Theorem
If 2 angles are supplements of the same angle (or congruent a…
20 terms
Geometry theorems
Midpoint
Bisector
Regular polygon
Corresponding angles postulate
The point on a segment equidistant from the segments endpoints
A point, line, ray, or plane which divides a segment, angle,…
All side measures and all angle measures are equal
(A)if two corresponding angles have the same measure, then th…
Midpoint
The point on a segment equidistant from the segments endpoints
Bisector
A point, line, ray, or plane which divides a segment, angle,…
13 terms
Geometry Theorems
If two lines are parallel, then
If two lines are parallel, then
If two lines are parallel, then
Vertical angles
alternate interior angles are congruent
corresponding angles are congruent
same side interior angles are congruent
are congruent
If two lines are parallel, then
alternate interior angles are congruent
If two lines are parallel, then
corresponding angles are congruent
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