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Math > Midterm > Flashcards

Midterm Flashcards

0
Q

Vertical Angels Congruence Theorem

A

All vertical angles are congruent

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1
Q

Right angle congruence theorem

A

All right angles are congruent

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2
Q

Linear Pair postulate

A

Angles In a linear pair are supplements

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3
Q

Parallel lines

A

Lines that don’t intersect and slopes are equal

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4
Q

Skew Lines

A

Do not intersect and aren’t on the same plane

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5
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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6
Q

Perpendicular postulate

A

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

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7
Q

Transversal

A

A line that intersects 2 or more other lines at different points

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8
Q

Interior angles

A

Inside the lines

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9
Q

Exterior angles

A

Outside the lines

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10
Q

Consecutive interior angles

A

Inside the lines and on the same side of the transversal

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11
Q

Alternate interior angels

A

Inside the lines and Opposite sides of the transversal

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12
Q

Alternate exterior angles

A

Outside the lines, opposite sides of the transversal

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13
Q

Corresponding angles

A

One inside one outside the lines, not adjacent (different intersections) same Sid of the transversal

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14
Q

Consecutive interior angles postulate

A

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

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15
Q

Alternate interior angles postulate

A

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

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16
Q

Corresponding angles postulate

A

Corresponding angles are congruent

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17
Q

Converse

A

Reversing (switching) the two parts of an if-then statements

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18
Q

Consecutive interior angles converse theorem

A

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

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19
Q

Alternate interior angles converse theorem

A

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

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20
Q

Alternate exterior angles converse theorem

A

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

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21
Q

Corresponding angles converse theorem

A

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

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22
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

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23
Q

Slope intercept of a line

A

Y=mx+b

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24
Q

Y intercept

A

B (as in y=mx+b)

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25
Q

Slope

A

Rise over run, change in y over change in x

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26
Q

H0Y VUX

A

Horizontal line, 0 slope, Y=#

Vertical line, undefined slope, x=#

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27
Q

Steepness

A

How fast the incline is rising(slope)

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28
Q

Slopes of parallel lines

A

Identical

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29
Q

Slopes of perpendicular lines

A

Opposite and reciprocal

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30
Q

Opposite reciprocals

A

Ex) 3/4 would be -4/3

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31
Q

Perpendicular transversal theorem

A

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

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32
Q

Scalene

A

No sides are congruent

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33
Q

Isosceles

A

2 sides are congruent

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34
Q

Equilateral

A

All three sides are congruent

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35
Q

Vertex

A

The angle created by two legs

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36
Q

Legs on an isosceles triangle

A

The two congruent sides

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37
Q

Isosceles base

A

The non-congruent side

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38
Q

Isosceles base angles

A

The 2 angles adjacent to the base

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39
Q

Acute triangle

A

All angles less than 90 degrees

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40
Q

Equiangular

A

All angles are congruent

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41
Q

Obtuse

A

One angle is greater than 90 degrees

42
Q

Right

A

One right angle

43
Q

Triangle sum theorem

A

The interior angles of a triangle add up to 180 degrees

44
Q

Corollary

A

An extension of a theorem/postulate

45
Q

Triangle sum corollary

A

The sum of the acute angles in a right triangle is 90 degrees

46
Q

Remote interior angles

A

The two interior angles not adjacent to the exterior angle

47
Q

Exterior angle theorem

A

The measure of an exterior angle equals the sum of the remote interior angles

48
Q

Congruent polygons

A

Have the same shape and size

49
Q

Corresponding parts of triangles

A

The same side or angle in 2 different triangles

50
Q

Congruent triangles

A

If 2 triangles have 3 pairs of congruent corresponding angles and 3 pairs of congruent corresponding sides, the triangles are congruent

51
Q

CPCTC

A

Corresponding parts of congruent triangles are congruent theorem.

52
Q

Symmetric property of congruent triangles

A

If triangle abc is congruent to triangle def, then def is congruent to abc

53
Q

Transitive property of congruent triangles

A

If abc is congruent to def, and def is congruent to jkl, then jkl is congruent to abc

54
Q

Reflexive property of congruent triangles

A

Abc is congruent to abc

55
Q

Third angle theorem

A

if 2 angles of a triangle are congruent to 2 angles of another triangle, then the third angles are automatically congruent

56
Q

What are the six ways to prove triangles congruent

A

CPCTC, SSS, SAS, AAA, AAS, HL

57
Q

Included angle

A

The angle between 2 sides

58
Q

Hypotenuse

A

The side across from the right angle

59
Q

Leg

A

The sides of the right triangle(not hypotenuse)

60
Q

Non-included side

A

A side not between 2 angles

61
Q

Base

A

The non-congruent side

62
Q

Base angles

A

The 2 angles adjacent to the base

63
Q

Base angle theorem

A

If 2 sides of a triangle are congruent, then the angles opposite from them are congruent

64
Q

Converse of the base angle theorem

A

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

65
Q

Mid segment of Triangle

A

Segment that connects midpoints of two sides of a triangle

66
Q

Mid segment theorem

A

The segments connecting the midpoints of two sides of a triangle are parallel and half as long as the third side

67
Q

Equidistant

A

A point the same distance from 2 points

68
Q

Perpendicular bisector

A

A segment that is perpendicular to the segment at its midpoint

69
Q

Perpendicular bisector theorem

A

If a point is on the perpendicular bisector of a segment then it is equidistant from the end points of a segment

70
Q

Converse of perpendicular theorem

A

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

71
Q

Angle bisector

A

A ray that divides an angle into two congruent adjacent angles(cuts it in half)

72
Q

Distance From a point to a line

A

The length of the perpendicular segment from a point to a line

73
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 an angle

74
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 of the angle.

75
Q

Altitude

A

A line segment that connects a vertex of a triangle with the opposite side,(or line containing the opposite side) and is perpendicular to that side

76
Q

Median

A

A line segment that connects a vertex of a triangle with the midpoint of the opposite side (3 per triangle)

77
Q

Triangle inequality theorem

A

A-b<a+b

78
Q

Ratios

A

Comparison of two numbers Using division

79
Q

Extended ratios

A

More than 2 numbers In a ratio

80
Q

Perimeter formula for a rectangle

A

2(x)+2(y)

81
Q

Area formula for a rectangle

A

(X)(y)

82
Q

Proportion

A

2 or more ratios in an equation

83
Q

Congruent polygons

A

Same size, same shape

84
Q

Similar(~) polygons

A

Corresponding angles are congruent and have same proportion, can be different sizes

85
Q

Statement of proportionality

A

Pretty much CPCTC

86
Q

Scale factor

A

The ratio of the lengths of two Corresponding sides

87
Q

Similarity of other lengths theorem

A

When all ratios turn out equal =

88
Q

AA similarity postulate

A

If 2 sets of corresponding angles are congruent then the triangles are similar

89
Q

SSS Similarity theorem

A

When you prove triangles similar by having all sides congruent

90
Q

SAS similarity theorem

A

When you prove triangles similar by having a side, angle, and side congruent

91
Q

Side splitter theorem

A

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

92
Q

Converse of the side splitter theorem

A

If a line divides two sides of a triangle proportionally, then it is parallel to the third side

93
Q

side splitter theorem extended

A

If three parallel lines intersect two transversals, then they divide the transversals proportionately

94
Q

Angle bisector theorem

A

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

95
Q

Radicand

A

The number under the radical

96
Q

Pythagorean theorem

A

A^2+b^2=c^2

97
Q

Pythagorean triples

A

Sets of positive numbers that satisfy the Pythagorean theorem

98
Q

Converse of the Pythagorean theorem

A

If the sum of the squares of the shorter sides of a triangle equals the square of the longest side, then it is a right triangle

99
Q

Acute triangle theorem

A

If the square of the longest side of a triangle is less than the sum of the squares of the other two sides, then the triangle is acute

100
Q

Obtuse triangle theorem

A

If the square of the longest side of a triangle is more than the sum of the squares of the other two sides, then the triangle is obtuse

101
Q

Complimentary angles

A

Adding up to 90 degrees

102
Q

Supplementary angles

A

Add up to 180 degrees

Math (5 decks)

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