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Geometry > Postulates and Theorems > Flashcards

Postulates and Theorems Flashcards

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
Q

Congruent Supplements Theorem

A

If two angles are supplementary to the same angle or congruent angles, then they are congruent

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26
Q

If two angles are supplementary to the same angle or congruent angles, then they are congruent

A

Congruent Supplements Theorem

27
Q

Congruent Complements Theorem

A

If two angles are complementary to the same angle or congruent angles, then they are congruent

28
Q

If two angles are complementary to the same angle or congruent angles, then they are congruent

A

Congruent Complements Theorem

29
Q

Linear Pair Postulate

A

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

30
Q

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

A

Linear Pair Postulate

31
Q

Vertical Angles Congruence Theorem

A

Vertical angles are always congruent

32
Q

Vertical angles are always congruent

A

Vertical Angles Congruence Theorem

33
Q

Parallel Postulate

A

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
Q

Perpendicular Postulate

A

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
Q

Corresponding Angles Theorem

A

If two parallel lines are cut by a transversal, then pairs of corresponding angles are congruent

36
Q

Alternate Interior Angles Theorem

A

If two parallel lines are cut by a transversal, then pairs of alternate interior angles are congruent

37
Q

Alternate Exterior Angles Theorem

A

If two parallel lines are cut by a transversal, then pairs of alternate exterior angles are congruent

38
Q

Consecutive Interior Angles Theorem

A

If two parallel lines are cut by a transversal, then pairs of consecutive interior angles are supplementary

39
Q

Corresponding Angles Converse

A

If two lines are cut by a transversal so airs of corresponding angles are congruent, then the two lines are parallel

40
Q

Alternate Interior Angles Converse

A

If two lines are cut by a transversal so airs of alternate interior angles are congruent, then the two lines are parallel

41
Q

Alternate Exterior Angles Converse

A

If two lines are cut by a transversal so airs of alternate exterior angles are congruent, then the two lines are parallel

42
Q

Consecutive Interior Angles Converse

A

If two lines are cut by a transversal so airs of consecutive interior angles are supplementary, then the two lines are parallel

43
Q

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

A

Parallel Postulate

44
Q

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

A

Perpendicular Postulate

45
Q

If two parallel lines are cut by a transversal, then pairs of corresponding angles are congruent

A

Corresponding Angles Theorem

46
Q

If two parallel lines are cut by a transversal, then pairs of alternate interior angles are congruent

A

Alternate Interior Angles Theorem

47
Q

If two parallel lines are cut by a transversal, then pairs of alternate exterior angles are congruent

A

Alternate Exterior Angles Theorem

48
Q

If two parallel lines are cut by a transversal, then pairs of consecutive interior angles are supplementary

A

Consecutive Interior Angles Theorem

49
Q

If two lines are cut by a transversal so pairs of alternate interior angles are congruent, then the two lines are parallel

A

Alternate Interior Angles Converse

49
Q

If two lines are cut by a transversal so pairs of corresponding angles are congruent, then the two lines are parallel

A

Corresponding Angles Converse

50
Q

If two lines are cut by a transversal so pairs of alternate exterior angles are congruent, then the two lines are parallel

A

Alternate Exterior Angles Converse

51
Q

If two lines are cut by a transversal so pairs of consecutive interior angles are supplementary, then the two lines are parallel

A

Consecutive Interior Angles Converse

52
Q

Transitive Property of Parallel Lines

A

If two lines are parallel to the same line, then they are parallel to each other

53
Q

Transitive Property of Perpendicular Lines

A

If two lines are perpendicular to the same line, then they are parallel to each other

54
Q

Perpendicular Transversal Theorem

A

In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line

55
Q

Lines Perpendicular to a Transversal Theorem

A

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other

56
Q

Slopes of Parallel Lines Theorem

A

In a coordinate plane, two lines are perpendicular if and only if they have the same slope

57
Q

Slopes of Perpendicular Lines Theorem

A

In a coordinate plane, two lines are perpendicular if and only if the product of their slopes is -1

58
Q

If two lines are parallel to the same line, then they are parallel to each other

A

Transitive Property of Parallel Lines

59
Q

If two lines are perpendicular to the same line, then they are parallel to each other

A

Transitive Property of Perpendicular Lines

60
Q

In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line

A

Perpendicular Transversal Theorem

61
Q

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other

A

Lines Perpendicular to a Transversal Theorem

62
Q

In a coordinate plane, two lines are parallel if and only if they have the same slope

A

Slopes of Parallel Lines Theorem

63
Q

In a coordinate plane, two lines are perpendicular if and only if the product of their slopes is -1

A

Slopes of Perpendicular Lines Theorem

Geometry (1 decks)

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