Studied by 1 person

0.0(0)

get a hint

hint

1

perpendicular lines

form right angles

New cards

2

diameters/radii and tangents

form right angles

New cards

3

corresponding sides of similar triangles are

in proportion

New cards

4

legs in an isosceles shape are

equal

New cards

5

if 2 parallel lines are cut by a transversal the alternate angles are

congruent

New cards

6

ø is

the measure of the central angle

New cards

7

an angle inscribed in a semi circle

is a right angle

New cards

8

base angles of any isosceles shape

are congruent

New cards

9

SOH

Sine Opposite (line segment opposite of the angle) Hypotenuse (line segment opposite right angle)

New cards

10

CAH

Cosine Adjacent (line segment between right angle and angle) Hypotenuse (line segment opposite right angle)

New cards

11

TOA

Tan Opposite (line segment opposite of the angle) Adjacent (line segment between right angle and angle)

New cards

12

Cosine and what other trigonometric ratio is complementary?

Sine

New cards

13

What are complementary angles?

angles that add up to 90 degrees

New cards

14

What are supplementary angles?

angles that add up to 180

New cards

15

inscribed angles are always half

of their arc

New cards

16

central angles are always =

to the arc they intercept

New cards

17

altitude

the length of the perpendicular line from a vertex to the opposite side of a figure. CONCURRENT AT THE ORTHOCENTER

New cards

18

bisect

divide (a line, angle, shape, etc.) into two equal parts.

New cards

19

Reflection y=x

(y,x)

New cards

20

Rotation -90º (x,y)

(y,-x)

New cards

21

Rotation 180 or -180 (x,y)

(-x,-y)

New cards

22

Reflection rx (x,y)

(x,-y) Reflect across the "X"-axis

New cards

23

Reflection ry (x,y)

(-x,y) reflect across the y-axis

New cards

24

Translation Tab (x,y)

(x+a,y+b) Move it "A" units horizontally and "B" units vertically

New cards

25

Reflection y=-x

(-y,-x)

New cards

26

Rotation 90º (x,y)

(-y,x)

New cards

27

point

a location in space with no length, width, or thickness

New cards

28

line

an infinately long set of points that has no width or thickness

New cards

29

ray

a portion of a line with one end point and including all points on one side of the end point

New cards

30

segment

a portion of a line bounded by two end points

New cards

31

plane

a flat set of points with no thickness that extends infinatelely in all directions

New cards

32

angle

a figure formed by two rays with a common endpoint

New cards

33

angle measure

the opening of an angle, measured in degrees or radians

New cards

34

linear pair

two adjacent angles that form a straight line (180º line)

New cards

35

vertical angles

the congruent opposite angles formed by intersecting lines

New cards

36

angle bisectors

divide angles into two congruent angles. CONCURRANT AT THE INCENTER

New cards

37

alternate interior angles

are congruent

New cards

38

same side interior angles

are supplementary

New cards

39

corresponding angles

are congruent

New cards

40

perpendicular bisector

a line, segment, or ray that is perpendicular to and bisects a segment. CONCURRENT AT THE CIRCUMCENTER

New cards

41

interior angle (of a polygon)

the angle inside the polygon formed by two adjacent sides

New cards

42

exterior angle (of a polygon)

the angle formed by a side and the extension of an adjacent side in a polygon

New cards

43

two examples of transformations that are neither rigid motions nor similarity transformations:e

horizontal stretch and vertical stretch

New cards

44

Horizontal stretch

elongates the figure only in the horizontal direction. On the coordinate plane, the x-coordinate of every point will be multiplied by a scale factor

New cards

45

Vertical stretch

elongates the figure only in the vertical direction. On the coordinate plane, the y-coordinate of every point will be multiplied by a scale factor

New cards

46

median

a segment from the vertex to the midpoint of th opposite side. CONCURRNT AT THE CENTROID

New cards

47

scalene triangles

no sides are congruent

New cards

48

isosceles

two legs and base angles are congruent

New cards

49

equilateral

three sides are congruent

New cards

50

All Of My Children Are Bringing In Peanut Butter Cookies

Altitudes/orthocenter. Medians/centroid. Angle bisectors/incenter. Perpindicular bisectors/circumcenter

New cards

51

Angle sum theorem

the sum of the measures of the interior angles = 180º

New cards

52

exterior angle theorem

the measure of any exterior angle of a triangle = the sum of the measures of the nonadjacent interior angles

New cards

53

isosceles triangle theorem and its converse

if two sides of a triangle are congruent, then the angles opposite them are congruent. if two angles in a triangle are congruent, then the sides opposite them are congruent

New cards

54

equilateral triangle theorem

all interior angles of an equilateral triangle measure 60º

New cards

55

Pythagorean theorem

In a right triangle, the sum of the squares of the legs equals the square of the hypotenuse

New cards

56

congruence

if two figures can be mapped onto another by a sequence of rigid motions.

New cards

57

reflexive property of equality

Any quality is equal to itself . For figures, any figure is congruent to itself

New cards

58

slope formula

Y2-Y1/X2-X1 (RISE/RUN)

New cards

59

Distance formula

√(X2-X1)squared+(Y2-Y1)squared

New cards

60

How to divide a segment proportionally

By using the two proportion ratios. X-X1/X2-X. Y-Y1/Y2-Y. and setting each of the proportions = to whatever the ratio that divides the line segment

New cards

61

how to find the area of a polygon on a graph

sketch a rectangle around the shape. find the areas of the triangles between the polygon and the rectangle. find all the areas of the triangles, add them up, and subtract them from the area of the rectangle.

New cards

62

collinear

three points are collinear if the slopes between any two pairs are equal

New cards

63

slope of a line= slope of perpendicular line

2/3=-3/2

New cards

64

segment parallel to a side theorem

-If a segment intersects two sides of a triangle such that a triangle similar to the OG triangle is formed, the segment is parallel to the third side

New cards

65

Side splitter theorem

A segment parallel to a side in a triangle divides the two sides it intersects proportionally

New cards

66

centroid theorem

the centroid of a triangle divides each median in a 1:2 ratio, with the longer segmant having a vertex as one of its endpoints

New cards

67

midsegment theorem

a segment joining the midpoints of two sides of a triangle (a midsegmant) is parallel to the opposite side, and it's length is equal to 1/2 the length of the opposite side

New cards

68

altitude to the hypotenuse of a right triangle theorem

the altitude to the hypotenuse of a right triangle forms two triangles that are similar to the O.G. triangle

New cards

69

parallelogram properties

Opposite sides are parallel and =. Opposite angles are congruent. adjacent angles are supplementary. The diagonals bisect each other.diagonals divide the parallelogram into two = triangle

New cards

70

trapezoid properties

one pair of parallel sides. Each lower base angle is supplementary to the upper base angle on the same side.

New cards

71

isosceles trapezoid properties

legs congruent, lower and upper base angles congruent, Any lower base angle is supplementary to any upper base angle, diagonals congruent

New cards

72

rectangle properties

parallelogram properties (opposite sides congruent). All right angles, diagonals are congruent

New cards

73

rhombus properties

parallel sides, opposite angles are congruent, consecutive angles are supplementary. all sides =. diagonals bisect angles.diagonals are perpindicular bisectors of each other DIAGNOLS FORM FOUR CONGRUENT ISOSCELES RIGHT TRIANGLES

New cards

74

square properties

(for proofs) any one of the parallelogram + square + rhombus properties

New cards

75

two lines are parallel

if the alternate interior angles formed are congruent

New cards

76

radius

a segment with one endpoint at the center of the circle and one endpoint on the circle

New cards

77

chord

a segment with both endpoints on the circle

New cards

78

diameter

a chord that passes through the center of the circle

New cards

79

secant

a line that intersects a circle at exactly two points

New cards

80

tangent

a line that intersects a circle at exactly at one point

New cards

81

point of tangency

the point at which a tangent intersects a circle

New cards

82

radii properties

all radii of a given circle are congruent, two circles are congruent if and only if their radii are congruent

New cards

83

central angle theorem

the angle measure of an arc equals the measure of the central angle that interceps the arc

New cards

84

inscribed angle theorem

the angle measure of an arc equals twice the measure of the inscribedangle that interceps the arc

New cards

85

congruence chord theorem

congruent chords intercept congruent arcs on a circle. congruent arcs on a circle are intercepted by congruent chords

New cards

86

parallel chord theorem

the two arcs formed between a pair of parallel chords are congruent. if the two arcs formed between a pair of chords are congruent then the chords are parallel.

New cards

87

chord-perpindicular bisector theorem

the perpendicular bisector of any chord passes through the center of the circle. a diameter or radius that is perpindicular to a chord bisects the chord. A diameter or radius that bisects a chord is perpindicular to the chord

New cards

88

tangent radius theorem

a diameter or radius to a point of tangency is perpindicular to the tangent. A line perpindicular to a tangent at the point of tangency passes through the center of the circle

New cards

89

congruent tangent theorem

given a circle and external point Q, segments between the external point and the two points of tangency are congruent

New cards

90

radian

π/180. A unit of angle measure. 2π is = to one complete revolution around a circle

New cards

91

Radian area

1/2Rsquared(ø)

New cards

92

major arc

an arc with a measurement greater than 180º

New cards

93

minor arc

an arc with a measurement less than 180º

New cards

94

semi-circular arc

an arc with a measurement of exactly 180º

New cards

95

angle of depression

the angle formed by the horizontal and the line of sight when looking downward to an object

New cards

96

angle of elevation

the angle formed by the horizontal and line of sight when looking upward an object

New cards

97

angle of rotation

the angle measure by which a figure or point spins around a center point

New cards

98

apex

the tip of a pyramid or cone or triangle

New cards

99

cavalieri's principle

if two solids are contained between two parallel planes, and every parallel plane between these two planes intercepts regions of equal area, then the solids have equal volume. Also, any two parallel planes intercept two solids of equal volume

New cards

100

center-radius equation of a circle

(x - h)squared + (y - k)squared = rsquared

New cards