Study sets matching "geometry theorems postulates"
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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…
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…
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…
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
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
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…
Angle addition postulate
Postulate
Postulate
postulate
M<AOB + M<BOC = M<AOC... Any angles added together
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 throu…
Angle addition postulate
M<AOB + M<BOC = M<AOC... Any angles added together
Postulate
a line contains at least two points a plane contains at least…
Postulate
Postulate
Postulate
Postulate
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
A line contains at least two points; a plane contains at least…
Postulate
Through any two points there is exactly one line
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
Postulate 1
Postulate 2
Postulate 3
Postulate 4
Ruler Postulate... 1.) the points on a line can be paired with t…
Segment addition postulate
Protractor Postulate
angle addition postulate
Postulate 1
Ruler Postulate... 1.) the points on a line can be paired with t…
Postulate 2
Segment addition postulate
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…
Postulate 5
Postulate 6
Postulate 7
Postulate 8
A line contains at least 2 points; a plane contains at least 3…
Through any two points there is exactly one line
Through any 3 points there is at least 1 plane, and through an…
If 2 points are in a plane, then the line that contains the po…
Postulate 5
A line contains at least 2 points; a plane contains at least 3…
Postulate 6
Through any two points there is exactly one line
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.
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…
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.
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
the points on the line can be paired with the real numbers in…
If B is between A and C, then AB + BC = AC
To find the measure of an angle, compute the absolute value of…
If point B is in the interior of <AOC, then m<AOB + m<BOC = m<…
Ruler Postulate
the points on the line can be paired with the real numbers in…
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
Points, Lines, and Planes Postulates (7)
Midpoint Theorem
Addition Property
Subtraction Property
- Through any two points there is exactly one line... - Through a…
If M is the midpoint of AB, then AM = MB
If a=b, then a+c=b+c
If a=b, then a-c=b-c
Points, Lines, and Planes Postulates (7)
- Through any two points there is exactly one line... - Through a…
Midpoint Theorem
If M is the midpoint of AB, then AM = MB
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…
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 1-1
Postulate 1-2
Postulate 1-3
Postulate 1-4
through any two points, there is exactly one line
if two distinct lines intersect, then they intersect in exactl…
if two distinct planes intersect, they intersect in exactly on…
through any three non-colinear points there is exactly one pla…
Postulate 1-1
through any two points, there is exactly one line
Postulate 1-2
if two distinct lines intersect, then they intersect in exactl…
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