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Geometry💀 > Proof definitions, postulates and theorems > Flashcards

Proof definitions, postulates and theorems Flashcards

1
Q

Addition Poe

A

If a = b, then

a+c=b+c

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2
Q

Perpendicular Lines

A

Meet at a right angle

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3
Q

Equilateral

A

A polygon where all sides are congruent

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4
Q

Equiangular

A

All angles are congruent

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5
Q

Subtraction Poe

A

If a = b, then

a-c=b-c

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6
Q

Multiplication Poe

A

If a = b, then

a(c)=b(c)

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7
Q

Division Poe

A

If a = b, then

a/c=b/c

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8
Q

Substitution Poe

A

If a = b, then

“a” can be substituted for “b” in any expression

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9
Q

Distributive Poe

A

If a = b, then

a(b+c)+ab+ac

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10
Q

Reflexive Poe

A

Basically, a thing equals itself

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11
Q

Symmetric Poe

A

Basically, if one expression equals another it doesn’t matter which expression goes on which side.

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12
Q

Transitive Poe

A

Basically, if two things equal a third thing, they also equal each other

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13
Q

Reflexive Poc

A

Basically, a thing(angle or side) is congruent to itself

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14
Q

Symmetric Poc

A

Basically, if one thing(angle or side) equals another it doesn’t matter which thing goes on which side

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15
Q

Transitive Poc

A

Basically, if two thing(angle or side) equal a third thing, they also equal each other

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16
Q

Right Angles Congruence Theorem

A

All right angles are congruent

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17
Q

Vertical Angles Congruence Theorem

A

All vertical angles are congruent

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18
Q

Linear Pair Postulate

A

Angles in a linear pair are supplements

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19
Q

Congruent Complements Theorem

A

If two angles are complementary to the same angle, they are congruent to each other

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20
Q

Congruent Complements Theorem

A

If two angles are supplementary to the same angle, they are congruent to each other

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21
Q

Parallel Postulate

A

given a line and a point not on the line, you can draw only one line that is parallel to the original line and goes through the point

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22
Q

Perpendicular Postulate

A

given a line and a point not on the line, you can draw only one line that is perpendicular to the original line and goes through the point

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23
Q

Transversal

A

a line that intersects two or more other lines at different points

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24
Q

Consecutive Interior Angles

A

Angles inside the lines and on the same side of the transversal

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25
Q

Alternate Interior Angles

A

Angles inside the lines and on opposite sides of the transversal

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26
Q

Alternate Exterior Angles

A

Angles outside the lines and opposite of the transversal

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27
Q

Corresponding Angles

A

Same corner of different intersections

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28
Q

Consecutive Interior Angles Postulate

A

For parallel lines crossed by a transversal, interior angles are supplementary

29
Q

Alternate Interior Angles Postulate

A

For parallel lines crossed by a transversal, alternate interior angles are congruent

30
Q

Alternate Exterior Angles Postulate

A

For parallel lines crossed by a transversal, alternate exterior angles are congruent

31
Q

Corresponding Angles Postulate

A

For parallel lines crossed by a transversal, corresponding angles are congruent

32
Q

If parallel lines are cut by a transversal…

A
  • Consecutive interior angles are supplementary

- Alternate interior, alternate exterior and corresponding angles are congruent

33
Q

Consecutive Interior Angles Converse Theorem

A

For lines cut by a transversal, if their consecutive interior angles are congruent then the lines are parallel

34
Q

Alternate Interior Angles Converse Theorem

A

For lines cut by a transversal, if their alternate interior angles are congruent then the lines are parallel

35
Q

Alternate Exterior Angles Converse Theorem

A

For lines cut by a transversal, if their alternate exterior angles are congruent then the lines are parallel

36
Q

Corresponding Angles Converse Theorem

A

For lines cut by a transversal, if their corresponding angles are congruent then the lines are parallel

37
Q

Transitive Property of Parallel Lines

A

If a is parallel to b and b is parallel to c, then a is parallel to c

38
Q

Linear Pair Perpendicular Theorem

A

If two lines intersect to form a pair of congruent angles, then the lines are perpendicular

39
Q

“Four Right Angles” Theorem

A

If two lines are perpendicular, then they intersect to form 4 right angles

40
Q

“Perpendicular Sides Complementary Angles” Theorem

A

If two sides of two adjacent angles are perpendicular, then the angles are complementary

41
Q

Perpendicular Transversal Theorem

A

If a transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other

42
Q

Lines perpendicular to the Transversal Theorem

A

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

43
Q

Triangle Sum Theorem

A

The angles of a triangle add up to 180 degrees

44
Q

Exterior Angles Theorem

A

The measure of an exterior angle equals the sum of the remote interior angle(the two interior angles NOT adjacent to the exterior angle)

45
Q

Definition of Congruent Triangles

A

If two triangles have 3 pairs of congruent corresponding angles and 3 pairs of congruent corresponding sides, the triangles are congruent

46
Q

CPCTC

A

Corresponding parts of congruent triangles are congruent

47
Q

SSS Postulate

A

If two triangles have 3 pairs of congruent corresponding sides, then the triangles are congruent

48
Q

SAS Postulate

A

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle then the two triangles are congruent

49
Q

Hypotenuse Leg Congruence Postulate

A

If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, the triangles are congruent

50
Q

ASA Postulate

A

If two angles and the included side(side in between two angles) of two triangles are congruent then the triangles are congruent

51
Q

AAS Postulate

A

If two angles and a non included side of two triangles are congruent then the triangles are congruent

52
Q

Base Angle Theorem

A

If two sides of triangles are congruent, then the angles opposite from them are congruent

53
Q

Converse of Base Angle Theorem

A

If two angles of a triangle are congruent, then the sides opposite from them are congruent

54
Q

Corollaries to Base Angle Theorem

A

If a triangle is equilateral, it is equiangular and if a triangle is equiangular, it is equilateral

55
Q

Midsegment Theorem

A

The segment connecting the midpoints of two sides of a triangle(the midsegment) is parallel to and half as long as the third side

56
Q

Perpendicular Bisector Theorem

A

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment

57
Q

Converse of Perpendicular Bisector Theorem

A

If a point is equidistant from the endpoints of a segment,, it is on the perpendicular bisector of a segment

58
Q

Angle Bisector Theorem

A

If a point is on the angle bisector of an angle then it is equidistant from the two sides of the angle

59
Q

Converse of Angle Bisector Theorem

A

If a point inside an angle is equidistant from the two sides of the angle then it is on the angle bisector

60
Q

Altitude

A

A line segment that connects a vertex of a triangle with the opposite side and is perp to that side

61
Q

Median

A

A line segment that connects a vertex of a triangle with the midpoint of the opposite side

62
Q

Triangle Inequality Theorem

A

Basically, if the third side is too short or too long, we end up with a line and not a triangle

63
Q

“All Lengths are Similar” Theorem

A

If two shapes are similar, all of their length-related measures are the same ratio as the scale factor

64
Q

AA Similarity Postulate

A

if two sets of corresponding angles of triangles are congruent, then the triangles are similar

65
Q

SSS Similarity Theorem

A

If the ratios of three pairs of corresponding sides are equal, then the triangles are similar

66
Q

SAS Similarity Postulate

A

If the ratio of two pairs of corresponding sides are equal AND the included angles are congruent, then the triangles are simialr

67
Q

Side Splitter Theorem

A

If a line parallel to one side of a triangle intersects the two other sides, then it divides the sides proportionally

68
Q

Extension of Side Splitter Theorem

A

If three parallel lines intersect two transversals then they divide the transversals proportionally

69
Q

Angle Bisector Theorem(for triangles)

A

If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to their adjacent sides

Geometry💀 (2 decks)

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