Study sets matching "geometry theorems postulates"
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Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
Points on a line can be matched one to one with real numbers t…
If B is between A and C, then AB + BC = AC.
Degrees on a protractor can be matched up one to one to repres…
If P is in the interior lf angle RST, then angle RSP + angle P…
Ruler Postulate
Points on a line can be matched one to one with real numbers t…
Segment Addition Postulate
If B is between A and C, then AB + BC = AC.
Postulate 1
Postulate 2
Postulate 3
Postulate 4
Ruler Postulate: The points on a line can be paired with the r…
Segment Addition Postulate: If B is between A and C, then AB +…
Protractor Postulate: On line AB in a given plane, choose any…
Angle Addition Postulate: If point B lies in the interior of <…
Postulate 1
Ruler Postulate: The points on a line can be paired with the r…
Postulate 2
Segment Addition Postulate: If B is between A and C, then AB +…
Angle-Side-Angle Congruence Theorem (AS…
Postulate
Theorem
Angle-Angle-Side Congruence Theorem (AA…
If two angles and a side between them are congruent in two dif…
A rule that we accept to be true.
A rule that has been proven to be true.
If two angles and a side not between them are congruent in two…
Angle-Side-Angle Congruence Theorem (AS…
If two angles and a side between them are congruent in two dif…
Postulate
A rule that we accept to be true.
Definition of Congruent
Definition of Midpoint
Definition of Bisector
Segment Addition Postulate
Segments are congruent if and only if the distance between the…
A point on a segment is the midpoint if it divides the segment…
A segment is bisected if and only if it is divided into 2 cong…
If B is between A and C (points must be collinear), then AB +…
Definition of Congruent
Segments are congruent if and only if the distance between the…
Definition of Midpoint
A point on a segment is the midpoint if it divides the segment…
Segment Addition postulate
Alternate Interior Angles Theorem
Alternate Exterior Angles Theorem
Same-Side Interior Angles Theorem
AB+BC=AC
If two parallel lines are cut by a transversal then the pair o…
If two parallel lines are cut by a transversal then the pair o…
If two parallel lines are cut by a transversal then the pair o…
Segment Addition postulate
AB+BC=AC
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal then the pair o…
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Addition Property of Equality
a = a
If a = b... Then b = a
If a = b, and b = c ... Then a = c
If a = b ... Then a + 3 = b + 3
Reflexive Property of Equality
a = a
Symmetric Property of Equality
If a = b... Then b = a
consecutive vertices (7)
diagonal (7)
Arc Addition Postulate (10)
Polygon Interior Angles Theorem (7)
two vertices that are endpoints of the same side
a segment that joins two non-consecutive vertices
The measure of an arc formed by two adjacent arcs is the sum o…
The sum of the measures of the interior angles of a convex n-g…
consecutive vertices (7)
two vertices that are endpoints of the same side
diagonal (7)
a segment that joins two non-consecutive vertices
Segment addition postulate
Angle addition postulate
Through any two points
Through any three points there is at le…
If B is between A and C, then AB + BC = AC.
If point B lies in the interior of angle AOC, then measurement…
Through any two points there is exactly one line
Through any three points there is at least one plane, and thro…
Segment addition postulate
If B is between A and C, then AB + BC = AC.
Angle addition postulate
If point B lies in the interior of angle AOC, then measurement…
Definition of Midpoint
Definition of Segment Bisector
Definition of Angle Bisector
Definition of Perpendicular
If D is the midpoint of AB then AD=DB (equal parts created).
If PM bisects AB, AM=MB.
If XB bisects angle ABC, then <ABX is congruent to <XBC
Perpendicular Lines form right angles.
Definition of Midpoint
If D is the midpoint of AB then AD=DB (equal parts created).
Definition of Segment Bisector
If PM bisects AB, AM=MB.
Postulate 1: Ruler Postulate
Postulate 2: Segment Addition Postulate
Postulate 4: The Angle Addition Postula…
Postulate 5
The points on a line can be paired in a one-to-one corresponde…
If B is between A and C, then AB + BC = AC
If point D is in the interior of angle ABC, then the m of angl…
Through any two points there is exactly one line.
Postulate 1: Ruler Postulate
The points on a line can be paired in a one-to-one corresponde…
Postulate 2: Segment Addition Postulate
If B is between A and C, then AB + BC = AC
coordinate midpoint property
segment additive property
angle addition property
linear pair theorem
if B is between A & C,... then AB+BC=AC
if D is on the interior of Angle ABC,... then m Angle ABD + m Ang…
if two angles form a linear pair,... then the two angles are supp…
coordinate midpoint property
segment additive property
if B is between A & C,... then AB+BC=AC
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Addition Property of Equality
a = a
If a = b... Then b = a
If a = b, and b = c ... Then a = c
If a = b ... Then a + 3 = b + 3
Reflexive Property of Equality
a = a
Symmetric Property of Equality
If a = b... Then b = a
Postulate
Corresponding Angles Postulate
Properties of a rhombus
Properties of a rectangle
Or axiom, is a statement that is accepted as true without proo…
If two parallel lines are cut by a transversal, then the pairs…
If a quadrilateral is a rhombus, then it is a parallelogram ... I…
If a quadrilateral is a rectangle, then it is a parallelogram…
Postulate
Or axiom, is a statement that is accepted as true without proo…
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pairs…
2: Postulate 5
2: Postulate 6
2: Postulate 7
2: Postulate 8
Through any two points there exists exactly one line
A line contains at least two points
If two lines intersect, then their intersection is exactly one…
Through any three non-collinear points there exists exactly on…
2: Postulate 5
Through any two points there exists exactly one line
2: Postulate 6
A line contains at least two points
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
If a = b, then a + c = b + c
If a = b, then a - c = b - c
If a = b, then (a)(c) = (b)(c)
If a = b, c not equal to "zero", then a/c = b/c
Addition Property of Equality
If a = b, then a + c = b + c
Subtraction Property of Equality
If a = b, then a - c = b - c
Equal Complements Theorem
Equal Supplements Theorem
Linear Pair Theorem
Vertical Angles Theorem
complements of the same (or equal) angle are equal in measure
supplements of the same (or equal) angle are equal in measure
if two angles for a linear pair, then the angles are supplemen…
vertical angles are congruent
Equal Complements Theorem
complements of the same (or equal) angle are equal in measure
Equal Supplements Theorem
supplements of the same (or equal) angle are equal in measure
Congruent Supplements Theorem
Congruent Complements Theorem
Theorem 1-4
Theorem 1-5
if two angles are supplementary to congruent angles they are c…
If two angles are complementary to congruent angles they are c…
All right angles are congruent
If two angles are congruent and supplementary, then each is a…
Congruent Supplements Theorem
if two angles are supplementary to congruent angles they are c…
Congruent Complements Theorem
If two angles are complementary to congruent angles they are c…
If a + b, then a + b = b + c
If a = b, then a - c = b - c
If a = b, then a(c) = b(c)
If a = b and c doesn't equal zero, then…
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of equality
Division Property of Equality
If a + b, then a + b = b + c
Addition Property of Equality
If a = b, then a - c = b - c
Subtraction Property of Equality
Midpoint Theorem (Theorem 2-1)
Angle Bisector Theorem (Theorem 2-2)
Definition of Complementary Angles
Definition of Supplementary Angles
If M is the midpoint of segment AB, then AM= 1/2AB and MB=1/2AB
If AB bisects angle CAD then the measure of angle CAB = 1/2 of…
Two angles' sum that adds up to 90 degrees
2 angles whose sum is 180
Midpoint Theorem (Theorem 2-1)
If M is the midpoint of segment AB, then AM= 1/2AB and MB=1/2AB
Angle Bisector Theorem (Theorem 2-2)
If AB bisects angle CAD then the measure of angle CAB = 1/2 of…
altitude of a triangle
circumcenter of a triangle
incenter of a triangle
orthocenter of a triangle
a perpendicular segment from a vertex to the line containing t…
the point of concurrency of the perpendicular bisectors of a t…
the point of concurrency of the angle bisectors of a triangle
the point of concurrency of the three altitudes of a triangle
altitude of a triangle
a perpendicular segment from a vertex to the line containing t…
circumcenter of a triangle
the point of concurrency of the perpendicular bisectors of a t…
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Addition Property of Equality
a = a
If a = b... Then b = a
If a = b, and b = c ... Then a = c
If a = b ... Then a + 3 = b + 3
Reflexive Property of Equality
a = a
Symmetric Property of Equality
If a = b... Then b = a
Through any two points, there is exactl…
Through any three non-collinear points,…
A line contains at least.........?
A plane contains at least..............…
Through any two points, there is exactly one line.
Through any three noncollinear points, there is exactly one pl…
A line contains at least two points
A plane contains at least three non-collinear points
Through any two points, there is exactl…
Through any two points, there is exactly one line.
Through any three non-collinear points,…
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 put into a one-to-one corresponden…
If B is between A and C, then AB + BC = AC
Given line AB and point O on line AB, all rays that can be dra…
If S is in the interior of <PQR, then m<PQS + m<SQR = m<PQR
Ruler Postulate
The points on a line can be put into a one-to-one corresponden…
Segment Addition Postulate
If B is between A and C, then AB + BC = AC