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Math II > Ch. 8 > Flashcards

Ch. 8 Flashcards

1
Q

Converse of Corresponding Angles Postulate

A

If 2 lines r intersected by a transversal, & corresponding angles are congruent, then the lines are parallel.

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2
Q

Converse of Cointerior Angles Theorem

A

If 2 lines r cut by a transv & cointerior angles r supp, then the lines r parallel

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3
Q

Converse of Alt Interior Angles Theorem

A

If 2 lines r cut by a transv & alt interior angles r congruent, then the lines r parallel

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4
Q

Perpendicular & Parallel Th

A

If 2 lines r perp 2 the same transversal, then they r parallel.

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5
Q

Perp & Transversal Th

A

If a transv is perp to one of two parallel lines, then it is also perp to the other line.

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6
Q

trapezoid

A

quadrilateral with only 1 pair of parallel sides

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7
Q

Triangle Sum Th

A

the sum of the measures of the angles of a triangle is 180

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8
Q

Quadrilateral Sum Th

A

The sum of the measures of the angles of a quadrilateral is 360.

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9
Q

Converse of Quadrilateral Th

A

If both pairs of opp angles of a quadrilateral r equal, then the quadrilateral is a parallelogram.

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10
Q

Exterior Angle Th

A

An exterior angle of a triangle is equal in measure to the sum of its 2 remote interior angles.

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11
Q

definition of similar

A

2 triangles are similar iff their vertices can be matched up so that the corresponding angles are equal & corresponding sides are in proportion.

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12
Q

definition of congruent

A

2 triangles r congruent iff their vertices can be matched up so that the corresponding parts (angles & sides) of the triangles r equal in measure.

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13
Q

Triangle Similarity Postulate (AA Post.)

A

If 2 angles of a triangle r equal to 2 angles of another triangle, then the 2 triangles are similar.

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14
Q

How to find any angle of a triangle?

A

A = 1/2ab sin C

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15
Q

trig

A

SOH CAH TOA

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16
Q

Overlapping Similar Triangles

A

If a line is drawn from a point on one side of a triangle parallel to another side, then it forms a triangle similar to the original side.

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17
Q

ASA Theorem

A

If 2 angles & the included side of 1 triangle are equal to the corresponding angles and side of another triangle, then the triangles are congruent.

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18
Q

AAS Theorem

A

If 2 angles and a non-included side of 1 triangle r equal to corresponding angles and side of another triangle, then the triangles are equal.

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19
Q

ASS

A

ASS IZ NOT GOOD

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20
Q

SAS Postulate

A

If 2 sides & the included angle of 2 triangle r equal to the corresponding sides & angle of another triangle, then the triangles r congruent.

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21
Q

angle bisector

A

a ray that begins in the vertex of an angle & divides the angle into 2 equal parts

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22
Q

segment bisector

A

a ray, line, or segment that divides a segment into two equal parts

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23
Q

perpendicular bisector

A

a line, ray, / segment that bisects the segment & is perpendicular to it

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24
Q

Hypotenuse-Leg Theorem

A

2 right triangles are equal if the hypotenuse & leg of 1 triangle are equal to the hypotenuse & leg of the other triangle

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25
Q

isosceles triangle

A

a triangle w/ 2 sides = in measure

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26
Q

equilateral triangle

A

a triangle in which all the sides are equal in measure

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27
Q

equiangular triangle

A

a triangle in which all the angles are equal in measure

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28
Q

Isosceles Triangle Theorem

A

If 2 sides of a triangle r = in measure, then the angles opposite those sides are = in measure

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29
Q

Converse of Isosceles Triangle Th

A

If 2 angles of a triangle r equal in measure, then the sides opposite those angles r = in measure

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30
Q

Equilateral Triangle Th

A

If a triangle is equilateral, then it’s also equiangular

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31
Q

Converse of Equil Triangle Th

A

If a triangle is equiangular, then it’s equilateral.

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32
Q

Perpendicular Bisector Th

A

If a point is the same distance from both ends of a segment, then it lies on the perp bisector of the segment

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33
Q

Similar Right Triangle Th

A

If the altitude is drawn to the hypotenuse of a right triangle, then the 2 triangles formed r similar to each other & the original triangle.

34
Q

geometric mean

A

If a, b, and x r positive numbers, and a/x = x/b, then x is the geometric mean b/w a and b. The GM is ALWAYS the pos root

35
Q

Geometric Mean Th

A

If the altitude is drawn to the hyp of a right triangle, then the msr of the altitude is the geometric mean b/w the measures of the parts of the hypotenuse.

36
Q

30-60-90

A

Opp 30 - x Hypotenuse - 2x Opp 60 - x[3

37
Q

45-45-90

A

Opp 45’s - x Hypotenuse - x[2

38
Q

trigonometry

A

SO-CAH-TOA

39
Q

sin, cos, and tan of 30

A

1/2, [3/2, [3/3 or 1/[3

40
Q

sin, cos, and tan of 60

A

[3/2, 1/2, [3

41
Q

sin, cos, and tan of 45

A

[2/2 or 1/[2, [2/2 or 1/[2, 1

42
Q

Pythagorean Theorem

A

In any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. c2 = a2 + b2

43
Q

If 2 lines r intersected by a transversal, & corresponding angles are congruent, then the lines are parallel.

A

Converse of Corresponding Angles Postulate

44
Q

If 2 lines r cut by a transv & cointerior angles r supp, then the lines r parallel

A

Converse of Cointerior Angles Theorem

45
Q

If 2 lines r cut by a transv & alt interior angles r congruent, then the lines r parallel

A

Converse of Alt Interior Angles Theorem

46
Q

If 2 lines r perp 2 the same transversal, then they r parallel.

A

Perpendicular & Parallel Th

47
Q

If a transv is perp to one of two parallel lines, then it is also perp to the other line.

A

Perp & Transversal Th

48
Q

quadrilateral with only 1 pair of parallel sides

49
Q

the sum of the measures of the angles of a triangle is 180

A

Triangle Sum Th

50
Q

The sum of the measures of the angles of a quadrilateral is 360.

A

Quadrilateral Sum Th

51
Q

If both pairs of opp angles of a quadrilateral r equal, then the quadrilateral is a parallelogram.

A

Converse of Quadrilateral Th

52
Q

An exterior angle of a triangle is equal in measure to the sum of its 2 remote interior angles.

A

Exterior Angle Th

53
Q

2 triangles are similar iff their vertices can be matched up so that the corresponding angles are equal & corresponding sides are in proportion.

A

definition of similar

54
Q

2 triangles r congruent iff their vertices can be matched up so that the corresponding parts (angles & sides) of the triangles r equal in measure.

A

definition of congruent

55
Q

If 2 angles of a triangle r equal to 2 angles of another triangle, then the 2 triangles are similar.

A

Triangle Similarity Postulate (AA Post.)

56
Q

If a line is drawn from a point on one side of a triangle parallel to another side, then it forms a triangle similar to the original side.

A

Overlapping Similar Triangles

57
Q

If 2 angles & the included side of 1 angle are equal to the corresponding angles and side of another triangle, then the angles are congruent.

A

ASA Theorem

58
Q

If 2 angles and a non-included side of 1 triangle r equal to corresponding angles and side of another triangle, then the triangles are equal.

A

AAS Theorem

59
Q

ASS IZ NOT GOOD

60
Q

If 2 sides & the included angle of 2 triangle r equal to the corresponding sides & angle of another triangle, then the triangles r congruent.

A

SAS Postulate

61
Q

a ray that begins in the vertex of an angle & divides the angle into 2 equal parts

A

angle bisector

62
Q

a ray, line, or segment that divides a segment into two equal parts

A

segment bisector

63
Q

a line, ray, / segment that bisects the segment & is perpendicular to it

A

perpendicular bisector

64
Q

2 right triangles are equal if the hypotenuse & leg of 1 triangle are equal to the hypotenuse & leg of the other triangle

A

Hypotenuse-Leg Theorem

65
Q

a triangle w/ 2 sides = in measure

A

isosceles triangle

66
Q

a triangle in which all the sides are equal in measure

A

equilateral triangle

67
Q

a triangle in which all the angles are equal in measure

A

equiangular triangle

68
Q

If 2 sides of a triangle r = in measure, then the angles opposite those sides are = in measure

A

Isosceles Triangle Theorem

69
Q

If 2 angles of a triangle r equal in measure, then the sides opposite those angles r = in measure

A

Converse of Isosceles Triangle Th

70
Q

If a triangle is equilateral, then it’s also equiangular

A

Equilateral Triangle Th

71
Q

If a triangle is equiangular, then it’s equilateral.

A

Converse of Equil Triangle Th

72
Q

If a point is the same distance from both ends of a segment, then it lies on the perp bisector of the segment

A

Perpendicular Bisector Th

73
Q

If the altitude is drawn to the hypotenuse of a right triangle, then the 2 triangles formed r similar to each other & the original triangle.

A

Similar Right Triangle Th

74
Q

If a, b, and x r positive numbers, and a/x = x/b, then x is the geometric mean b/w a and b. The GM is ALWAYS the pos root

A

geometric mean

75
Q

If the altitude is drawn to the hyp of a right triangle, then the msr of the altitude is the geometric mean b/w the measures of the parts of the hypotenuse.

A

Geometric Mean Th

76
Q

Opp 30 - x Hypotenuse - 2x Opp 60 - x[3

77
Q

Opp 45’s - x Hypotenuse - x[2

78
Q

SO-CAH-TOA

A

trigonometry

79
Q

1/2, [3/2, [3/3 or 1/[3

A

sin, cos, and tan of 30

80
Q

[3/2, 1/2, [3

A

sin, cos, and tan of 60

81
Q

[2/2 or 1/[2, [2/2 or 1/[2, 1

A

sin, cos, and tan of 45

82
Q

In any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. c2 = a2 + b2

A

Pythagorean Theorem

Math II (17 decks)

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