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 +…
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…
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.
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…
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 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
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
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…
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…
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…
Corresponding Angles
Corresponding Angles Converse
Alternate Interior Angles
Alternate Exterior Angles
If two parallel lines are cut by a transversal, then the pairs…
If two lines are cut by a transversal and the corresponding an…
If two parallel lines are cut by a transversal, then the alter…
If two parallel lines are cut by a transversal, then the alter…
Corresponding Angles
If two parallel lines are cut by a transversal, then the pairs…
Corresponding Angles Converse
If two lines are cut by a transversal and the corresponding an…
Theorem 5.3 (Circumcenter Theorem)
Theorem 5.4 (Angle Bisector Theorem)
Theorem 5.5 (Converse of the Angle Bise…
Theorem 5.6 (Incenter Theorem)
The perpendicular bisectors of a triangle intersect at a point…
If a point is on the bisectors of an angle, then it is equidis…
If a point in the interior of an angle is equidistant from the…
The angle bisectors of a triangle intersect at a point called…
Theorem 5.3 (Circumcenter Theorem)
The perpendicular bisectors of a triangle intersect at a point…
Theorem 5.4 (Angle Bisector Theorem)
If a point is on the bisectors of an angle, then it is equidis…
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
Theorem 5.1 (perpendicular Bisector The…
Theorem 5.2 (Converse of the Perpendicu…
Theorem 5.3 (Circumcenter Theorem)
Theorem 5.4 (Angle Bisector Theorem)
If a point is on the perpendicular bisector of a segment then…
If a point is equidistant from the endpoints of a segment then…
The perpendicular bisectors of a triangle intersect at a point…
If a point is on the bisector of an angle, then it is equidist…
Theorem 5.1 (perpendicular Bisector The…
If a point is on the perpendicular bisector of a segment then…
Theorem 5.2 (Converse of the Perpendicu…
If a point is equidistant from the endpoints of a segment then…
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
Perp bisector theorem
concurrence of perp bisectors
Concurrence of Angle Bisectors
The triangle congruence postulates
each point on the perpendicular bisector of a segment is equid…
in any triangle the perp bisectors of the sodes and concurrent…
in any triangle the angle bisectors are concurrent ( meeting a…
if two triangles share the following triplets of congruent cor…
Perp bisector theorem
each point on the perpendicular bisector of a segment is equid…
concurrence of perp bisectors
in any triangle the perp bisectors of the sodes and concurrent…
postulate
theorem
Postulate 2-1
Postulate 2-2
accepted as true without proof
a true statement that follows as a result of other true statem…
through any two points, there is exactly one line
through three non-collinear points, there is exactly one plane
postulate
accepted as true without proof
theorem
a true statement that follows as a result of other true statem…
Theorem 4.1
Side-side-side (SSS)
Side-angle-side (SAS)
Angle-side-angle (ASA)
If 2 angles of one triangle are congruent to 2 angles of anoth…
three sides of one triangle are equal to three sides of another
If two sides and the included angle of one triangle are congru…
Two angles and the included side are congruent
Theorem 4.1
If 2 angles of one triangle are congruent to 2 angles of anoth…
Side-side-side (SSS)
three sides of one triangle are equal to three sides of another
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…
Justification that angles/segments are…
Justification that angles are congruent…
Justification that angles are congruent…
Justification that angles are congruent…
Corresponding parts of corresponding figures are congruent
If two parallel lines are cut by a transversal, then the corre…
If ray BD is the bisector of ∠ABC, then ∠ABD ≅ ∠DBC.
Two angles are congruent iff they have the same measure.... - If…
Justification that angles/segments are…
Corresponding parts of corresponding figures are congruent
Justification that angles are congruent…
If two parallel lines are cut by a transversal, then the corre…