Geometry Regents Plagiarized (not really lol)

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173 Terms

1

perpendicular lines

form right angles

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2

diameters/radii and tangents

form right angles

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3

corresponding sides of similar triangles are

in proportion

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4

legs in an isosceles shape are

equal

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5

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

congruent

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6

ø is

the measure of the central angle

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7

an angle inscribed in a semi circle

is a right angle

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8

base angles of any isosceles shape

are congruent

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9

SOH

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

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10

CAH

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

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11

TOA

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

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12

Cosine and what other trigonometric ratio is complementary?

Sine

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13

What are complementary angles?

angles that add up to 90 degrees

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14

What are supplementary angles?

angles that add up to 180

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15

inscribed angles are always half

of their arc

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16

central angles are always =

to the arc they intercept

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17

altitude

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

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18

bisect

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

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19

Reflection y=x

(y,x)

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20

Rotation -90º (x,y)

(y,-x)

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21

Rotation 180 or -180 (x,y)

(-x,-y)

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22

Reflection rx (x,y)

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

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23

Reflection ry (x,y)

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

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24

Translation Tab (x,y)

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

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25

Reflection y=-x

(-y,-x)

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26

Rotation 90º (x,y)

(-y,x)

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27

point

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

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28

line

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

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29

ray

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

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30

segment

a portion of a line bounded by two end points

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31

plane

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

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32

angle

a figure formed by two rays with a common endpoint

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33

angle measure

the opening of an angle, measured in degrees or radians

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34

linear pair

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

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35

vertical angles

the congruent opposite angles formed by intersecting lines

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36

angle bisectors

divide angles into two congruent angles. CONCURRANT AT THE INCENTER

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37

alternate interior angles

are congruent

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38

same side interior angles

are supplementary

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39

corresponding angles

are congruent

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40

perpendicular bisector

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

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41

interior angle (of a polygon)

the angle inside the polygon formed by two adjacent sides

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42

exterior angle (of a polygon)

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

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43

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

horizontal stretch and vertical stretch

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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

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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

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46

median

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

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47

scalene triangles

no sides are congruent

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48

isosceles

two legs and base angles are congruent

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49

equilateral

three sides are congruent

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50

All Of My Children Are Bringing In Peanut Butter Cookies

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

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51

Angle sum theorem

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

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52

exterior angle theorem

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

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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

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54

equilateral triangle theorem

all interior angles of an equilateral triangle measure 60º

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55

Pythagorean theorem

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

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56

congruence

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

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57

reflexive property of equality

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

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58

slope formula

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

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59

Distance formula

√(X2-X1)squared+(Y2-Y1)squared

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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

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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.

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62

collinear

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

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63

slope of a line= slope of perpendicular line

2/3=-3/2

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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

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65

Side splitter theorem

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

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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

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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

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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

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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

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70

trapezoid properties

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

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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

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72

rectangle properties

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

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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

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74

square properties

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

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75

two lines are parallel

if the alternate interior angles formed are congruent

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76

radius

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

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77

chord

a segment with both endpoints on the circle

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78

diameter

a chord that passes through the center of the circle

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79

secant

a line that intersects a circle at exactly two points

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80

tangent

a line that intersects a circle at exactly at one point

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81

point of tangency

the point at which a tangent intersects a circle

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82

radii properties

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

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83

central angle theorem

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

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84

inscribed angle theorem

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

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85

congruence chord theorem

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

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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.

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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

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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

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89

congruent tangent theorem

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

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90

radian

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

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91

Radian area

1/2Rsquared(ø)

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92

major arc

an arc with a measurement greater than 180º

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93

minor arc

an arc with a measurement less than 180º

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94

semi-circular arc

an arc with a measurement of exactly 180º

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95

angle of depression

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

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96

angle of elevation

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

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97

angle of rotation

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

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98

apex

the tip of a pyramid or cone or triangle

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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

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100

center-radius equation of a circle

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

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