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Geometry > Postulates and Theorems > Flashcards

Postulates and Theorems Flashcards

(64 cards)

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1
Q

Ruler Postulate

A

The points on a line can all be matched one-to-one with real numbers.

Distance =|point A’s coordinate - point B’s coordinate-|

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2
Q

Segment Addition Postulate

A

If B is between A and , then AB + BC = AC and AC = AB + BC.

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3
Q

Protractor Postulate

A

The rays of an angle can be matched one-to-one with real numbers 0-180.

Measure = |ray A’s number - ray B’s number|

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4
Q

Angle Addition Postulate

A

If P is in the interior of ∠RST, then ⅿ∠RST = ⅿ∠RSP + ⅿ∠PST.

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5
Q

Two Point Postulate

A

Through any two distinct points, there exists exactly one line.

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6
Q

Line-Point Postulate

A

A line contains at least two points.

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7
Q

Line Intersection Postulate

A

If two lines intersect, then their intersection is exactly one point.

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8
Q

Three Point Postulate

A

Through any three noncolinear points, there exists exactly one plane.

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9
Q

Plane-Point Postulate

A

A plane contains at least three noncolinear points.

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10
Q

Plane-Line Postulate

A

If two points lie in a plane, then the line containing them lies in the same plane.

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11
Q

Plane Intersection Postulate

A

If two planes intersect, then their intersection is a line.

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12
Q

The points on a line can all be matched one-to-one with real numbers.

Distance =|point A’s coordinate - point B’s coordinate-|

A

Ruler Postulate

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13
Q

If B is between A and , then AB + BC = AC and AC = AB + BC.

A

Segment Addition Postulate

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14
Q

The rays of an angle can be matched one-to-one with real numbers 0-180.

Measure = |ray A’s number - ray B’s number|

A

Protractor Postulate

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15
Q

If P is in the interior of ∠RST, then ⅿ∠RST = ⅿ∠RSP + ⅿ∠PST.

A

Angle Addition Postulate

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16
Q

Through any two distinct points, there exists exactly one line.

A

Two Point Postulate

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17
Q

A line contains at least two points.

A

Line-Point Postulate

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18
Q

If two lines intersect, then their intersection is exactly one point.

A

Line Intersection Postulate

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19
Q

Through any three noncolinear points, there exists exactly one plane.

A

Three Point Postulate

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20
Q

A plane contains at least three noncolinear points.

A

Plane-Point Postulate

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21
Q

If two points lie in a plane, then the line containing them lies in the same plane.

A

Plane-Line Postulate

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22
Q

If two planes intersect, then their intersection is a line.

A

Plane Intersection Postulate

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23
Q

Right Angle Congruence Theorem

A

All right angles are congruent

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24
Q

All right angles are congruent

A

Right Angle Congruence Theorem

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25
Congruent Supplements Theorem
If two angles are supplementary to the same angle or congruent angles, then they are congruent
26
If two angles are supplementary to the same angle or congruent angles, then they are congruent
Congruent Supplements Theorem
27
Congruent Complements Theorem
If two angles are complementary to the same angle or congruent angles, then they are congruent
28
If two angles are complementary to the same angle or congruent angles, then they are congruent
Congruent Complements Theorem
29
Linear Pair Postulate
If two angles form a linear pair, then they are supplementary
30
If two angles form a linear pair, then they are supplementary
Linear Pair Postulate
31
Vertical Angles Congruence Theorem
Vertical angles are always congruent
32
Vertical angles are always congruent
Vertical Angles Congruence Theorem
33
Parallel Postulate
If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line
34
Perpendicular Postulate
If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line
35
Corresponding Angles Theorem
If two parallel lines are cut by a transversal, then pairs of corresponding angles are congruent
36
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then pairs of alternate interior angles are congruent
37
Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then pairs of alternate exterior angles are congruent
38
Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal, then pairs of consecutive interior angles are supplementary
39
Corresponding Angles Converse
If two lines are cut by a transversal so airs of corresponding angles are congruent, then the two lines are parallel
40
Alternate Interior Angles Converse
If two lines are cut by a transversal so airs of alternate interior angles are congruent, then the two lines are parallel
41
Alternate Exterior Angles Converse
If two lines are cut by a transversal so airs of alternate exterior angles are congruent, then the two lines are parallel
42
Consecutive Interior Angles Converse
If two lines are cut by a transversal so airs of consecutive interior angles are supplementary, then the two lines are parallel
43
If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line
Parallel Postulate
44
If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line
Perpendicular Postulate
45
If two parallel lines are cut by a transversal, then pairs of corresponding angles are congruent
Corresponding Angles Theorem
46
If two parallel lines are cut by a transversal, then pairs of alternate interior angles are congruent
Alternate Interior Angles Theorem
47
If two parallel lines are cut by a transversal, then pairs of alternate exterior angles are congruent
Alternate Exterior Angles Theorem
48
If two parallel lines are cut by a transversal, then pairs of consecutive interior angles are supplementary
Consecutive Interior Angles Theorem
49
If two lines are cut by a transversal so pairs of alternate interior angles are congruent, then the two lines are parallel
Alternate Interior Angles Converse
49
If two lines are cut by a transversal so pairs of corresponding angles are congruent, then the two lines are parallel
Corresponding Angles Converse
50
If two lines are cut by a transversal so pairs of alternate exterior angles are congruent, then the two lines are parallel
Alternate Exterior Angles Converse
51
If two lines are cut by a transversal so pairs of consecutive interior angles are supplementary, then the two lines are parallel
Consecutive Interior Angles Converse
52
Transitive Property of Parallel Lines
If two lines are parallel to the same line, then they are parallel to each other
53
Transitive Property of Perpendicular Lines
If two lines are perpendicular to the same line, then they are parallel to each other
54
Perpendicular Transversal Theorem
In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line
55
Lines Perpendicular to a Transversal Theorem
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other
56
Slopes of Parallel Lines Theorem
In a coordinate plane, two lines are perpendicular if and only if they have the same slope
57
Slopes of Perpendicular Lines Theorem
In a coordinate plane, two lines are perpendicular if and only if the product of their slopes is -1
58
If two lines are parallel to the same line, then they are parallel to each other
Transitive Property of Parallel Lines
59
If two lines are perpendicular to the same line, then they are parallel to each other
Transitive Property of Perpendicular Lines
60
In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line
Perpendicular Transversal Theorem
61
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other
Lines Perpendicular to a Transversal Theorem
62
In a coordinate plane, two lines are parallel if and only if they have the same slope
Slopes of Parallel Lines Theorem
63
In a coordinate plane, two lines are perpendicular if and only if the product of their slopes is -1
Slopes of Perpendicular Lines Theorem

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