Study sets matching "geometry theorems"

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Study sets matching "geometry theorems"

34 terms
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
51 terms
Geometry Theorems
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°
20 terms
Theorems Geometry
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…
Theorems Geometry
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…
16 terms
Geometry Theorems
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"
33 terms
Geometry Theorems
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?
Geometry Theorems
corresponding angles converse
alternating interior angles converse
alternate exterior angles converse
consecutive interior angles converse
corresponding angles converse
alternating interior angles converse
22 terms
geometry theorems
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…
Geometry Theorems
Congruent Supplement Theorem
Congruent Complement Theorem
Right Angle Theorem
Vertical Angle Theorem
...
...
...
...
Congruent Supplement Theorem
...
Congruent Complement Theorem
...
16 terms
Geometry Theorems
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…
Geometry Theorems
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…
Geometry Theorems
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…
34 terms
Geometry theorems
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
Geometry Theorems
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…
5 terms
Geometry Theorems
add
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47 terms
Geometry theorems
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…
9 terms
Geometry Theorems
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…
Geometry theorems
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…
9 terms
Theorems geometry
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…
Geometry theorems
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
26 terms
Geometry theorems
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…
7 terms
geometry theorems
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
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…
Geometry theorems
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
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.
Geometry Theorems
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
Geometry Theorems
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…
23 terms
Geometry Theorems
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…
8 terms
Geometry THEOREMS
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
8 terms
Geometry Theorems
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…
Geometry Theorems
Distance formula
Midpoint formula
Slope formula
Slope intercept formula
Distance formula
Midpoint formula
Geometry theorems
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…
6 terms
Geometry Theorems
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…
Geometry Theorems
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
Geometry theorems
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
15 terms
Geometry Theorems
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…
Geometry theorems
=90
Acute
Obtuse
Equilateral
Right
0<x<90
90<x<180
All = sides
=90
Right
Acute
0<x<90
Geometry Theorems
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
25 terms
Geometry theorems
Theorem 2-1
Theorem 2-2
Theorem 2-3
Theorem 2-4
Vertical angles theorem
Congruent supplements theorem
Congruent complements theorem
All right angles are congruent
Theorem 2-1
Vertical angles theorem
Theorem 2-2
Congruent supplements theorem
14 terms
Geometry Theorems
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
Geometry Theorems
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
20 terms
Geometry Theorems
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…
16 terms
Theorems (Geometry)
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
Geometry theorems
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…
Geometry Theorems
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…
Geometry theorems
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…
Geometry Theorems
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
Geometry theorems
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…
Geometry Theorems
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
Geometry - Theorems
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
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