#### Study sets matching "geometry theorems postulates"

#### Study sets matching "geometry theorems postulates"

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…

Postulate 3-1 Same-side Interior Angle…

Theorem 3-1 Alternate Interior Angles T…

Theorem 3-2 Corresponding Angles Theore…

Theorem 3-3 Alternate Exterior Angles T…

supplementary... m∠1 + m∠2 = 180

congruent

corresponding

exterior

Postulate 3-1 Same-side Interior Angle…

supplementary... m∠1 + m∠2 = 180

Theorem 3-1 Alternate Interior Angles T…

congruent

Corresponding Angles Postulate - If two…

Alternate Interior Angles Theorem - If…

Alternate Exterior Angles Theorem - If…

Same-Side Interior Angles Theorem - If…

then the pairs of corresponding angles are congruent.

then the alternate interior angles are congruent.

then the alternate exterior angles are congruent.

then the pairs of same-side interior angles are supplementary.

Corresponding Angles Postulate - If two…

then the pairs of corresponding angles are congruent.

Alternate Interior Angles Theorem - If…

then the alternate interior angles are congruent.

Side-Side-Side (SSS) Congruence

Side-Angle-Side (SAS) Congruence

Angle-Side-Angle (ASA) Congruence

Angle-Angle-Side (AAS) Congruence

If three sides of one triangle are congruent to three sides of…

If two sides and the included angle of one triangle are congru…

If two angles and the included side of one triangle are congru…

If two angles and the non-included side of one triangle are co…

Side-Side-Side (SSS) Congruence

If three sides of one triangle are congruent to three sides of…

Side-Angle-Side (SAS) Congruence

If two sides and the included angle of one triangle are congru…

Radius

Chords

Tangents

Arcs

In a circle, a radius perpendicular to a chord bisects the cho…

In a circle, or congruent circles, congruent chords are equidi…

Tangent segments to a circle from the same external point are…

In the same circle, or congruent circles, congruent central an…

Radius

In a circle, a radius perpendicular to a chord bisects the cho…

Chords

In a circle, or congruent circles, congruent chords are equidi…

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…

Expansion Postulate

Line Postulate

Plane Postulate

Flat Plane Postulate

A line contains at least two points. A plane contains at least…

Any two points in space lie in exactly one line

Three distinct noncollinear points lie in exactly one plane

If two points lie in a plane, then the line containing these t…

Expansion Postulate

A line contains at least two points. A plane contains at least…

Line Postulate

Any two points in space lie in exactly one line

Conditional

Converse

Inverse

Contrapositive

p→q; if p then q; equivalent to Contrapositive

q→p; if q then p; equivalent to Inverse

~p→~q; if not p then not q; equivalent to Converse

~q→~p; if not q then not p; equivalent to Conditional

Conditional

p→q; if p then q; equivalent to Contrapositive

Converse

q→p; if q then p; equivalent to Inverse

Parallelograms- About Sides

Parallelograms- About Angles

Parallelograms- About Diagonals

Parallelogram Converses- About Sides

If a quadrilateral is a parallelogram, the opposite... sides are…

* If a quadrilateral is a parallelogram, the opposite... angles…

* If a quadrilateral is a parallelogram, the diagonals... bisect…

* If both pairs of opposite sides of a quadrilateral... are para…

Parallelograms- About Sides

If a quadrilateral is a parallelogram, the opposite... sides are…

Parallelograms- About Angles

* If a quadrilateral is a parallelogram, the opposite... angles…

there is exactly one line.

there is exactly one plane.

two points.

three noncollinear points.

Through any two points,

Through any three noncollinear points,

A line contains at least

A plane contains at least

there is exactly one line.

Through any two points,

there is exactly one plane.

Through any three noncollinear points,

theorem

postulate

definition

segment bisector

a statement that can be proved

something we don't need to prove, uses past information to bas…

assigns a term to an object. are always reversible

segment,ray,line, plane that divides a segment into two congru…

theorem

a statement that can be proved

postulate

something we don't need to prove, uses past information to bas…

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

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 noncollinear points.

Postulate 2.1

Through any two points, there is exactly one line.

Postulate 2.2

Through any three noncollinear points, there is exactly one pl…

undefined term

point

line

plane

a word without a formal definition

undefined, a location with no size or dimension

undefined, a series of infinite points that extends in two dir…

undefined, flat surface that has no thickness and extends in a…

undefined term

a word without a formal definition

point

undefined, a location with no size or dimension

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

Congruent Right Angles Theorem

Vertical angles are congruent.

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

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

All right angles are congruent.

Vertical Angles Theorem

Vertical angles are congruent.

Congruent Supplements Theorem

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

Angle Addition Postulate

Segment Addition Postulate

Pythagorean Theorem

Linear Pair Theorem

If S is in the interior of PQR, then mPQS + mSQR = m PQR. (bas…

If B is between A & C, then AB + BC = AC. (basically means: 2…

In a right triangle, leg squared + leg squared = hypotenuse sq…

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

Angle Addition Postulate

If S is in the interior of PQR, then mPQS + mSQR = m PQR. (bas…

Segment Addition Postulate

If B is between A & C, then AB + BC = AC. (basically means: 2…

Postulate 1

Postulate 2

Postulate 3

Postulate 4

A line contains at least 2 points;... A plane contains at least 3…

Through any 2 points there is exactly one line.

Through any 3 points there is at least 1 plane, and through an…

If 2 points are a plane, then the line that contains the point…

Postulate 1

A line contains at least 2 points;... A plane contains at least 3…

Postulate 2

Through any 2 points there is exactly one line.

Parallel Lines

Perpendicular Lines

Skew Lines

Parallel Planes

Are coplanar lines and do not intersect.

Lines that intersect at 90 degree angles.

Lines that are not coplanar, not parallel, and do not intersec…

Are planes that do not intersect.

Parallel Lines

Are coplanar lines and do not intersect.

Perpendicular Lines

Lines that intersect at 90 degree angles.

Side-Side-Side (SSS)

Side-Angle-Side (SAS)

Angle-Side-Angle (ASA)

Angle-Angle-Side (AAS)

If three sides of one triangle are congruent to the second tri…

If two sides and the included angle of one triangle are congru…

If two sides and the included side of one triangle are congrue…

If two angles and a non included side of one triangle are cong…

Side-Side-Side (SSS)

If three sides of one triangle are congruent to the second tri…

Side-Angle-Side (SAS)

If two sides and the included angle of one triangle are congru…

one plane is two points

two plane is 3 points

2 points on a line

3 points on a plane

Through any 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 noncollinear points

one plane is two points

Through any points, there is exactly one line

two plane is 3 points

Through any three noncollinear points, there is exactly one pl…

Postulate 1

Postulate 4

Postulate 5

Postulate 6

(Segment Addition Postulate)... if B is between A and C, then AB+…

(Angle Addition Postulate)... if B lies in the interior of <AOC,…

a LINE contains at least 2 POINTS... a PLANE contains at least 3…

through any 2 POINTS there is exactly 1 LINE

Postulate 1

(Segment Addition Postulate)... if B is between A and C, then AB+…

Postulate 4

(Angle Addition Postulate)... if B lies in the interior of <AOC,…

Definition of Supplementary Angles

Definition of Alternate Interior Angles

Definition of Alternate Exterior angles

Definition of Corresponding Angles

2 angles whose measures have a sum of 180 degrees

2 non-adjacent angles that lie on opposite sides of the transv…

2 angles who are on opposite sides of the transversal and outs…

2 angles who are on the same side of the transversal and the s…

Definition of Supplementary Angles

2 angles whose measures have a sum of 180 degrees

Definition of Alternate Interior Angles

2 non-adjacent angles that lie on opposite sides of the transv…

Postulate 5

Postulate 6

Postulate 7

Postulate 8

A line contains at least two points; a plane contains at least…

Through any two points there is exactly one line

Through any three points there is at least one plane, and thro…

If two points are in a plane, then the line that contains the…

Postulate 5

A line contains at least two points; a plane contains at least…

Postulate 6

Through any two points there is exactly one line

Segment addition postulate

Angle addition postulate

Definition of midpoint

Definition of angle bisector

If Q is between P and R, then PR + QR = PR

If F is the interior of angle CDE, then angle CDF + angle FDE…

A segment or point that bisects a segment into two congruent s…

A segment or point that bisects an angle into two congruent an…

Segment addition postulate

If Q is between P and R, then PR + QR = PR

Angle addition postulate

If F is the interior of angle CDE, then angle CDF + angle FDE…