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2022-2023 > Geometry Regents Review > Flashcards

Geometry Regents Review Flashcards

1
Q

Sum of Interior Angles

A

180 (n - 2)

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2
Q

Each Interior Angle of a Regular Polygon

A

(180(n-2))/n

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3
Q

Sum of Exterior Angles

A

360

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4
Q

Each Exterior Angle

A

360/n

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5
Q

Midsegment on a Triangle:
- What is it?
- Relationship to the third side?
- What does it do to the triangle?

A
  • A segment joining the midpoints
  • 1/2 the length of the third side
  • Splits the triangle into two similar triangles
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6
Q

Standard Form of a Line

A

y=mx+b

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7
Q

Slope Formula

A

m=(y2-y1)/(x2-x1)

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8
Q

Parallel Lines

A

same slope, different y-intercepts

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9
Q

Perpendicular Lines

A

negative reciprocal slopes

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10
Q

Collinear Points

A

same line

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11
Q

Midpoint Formula

A

M = (((x1+x2)/2), ((y1+y2)/2)))

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12
Q

Distance Formula

A

d = √(x2 − x1)^2 + (y2 − y1)^2

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13
Q

New X-Coordinate

A

x1+(r1/(r1+r2))(x2-x1)

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14
Q

New Y-Coordinate

A

y1+(r1/(r1+r2))(y2-y1)

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15
Q

Triangle Inequality Theorems
- sum of two sides
- difference of two sides
- longest side opposite of
- shortest side opposite of

A
  • The sum of 2 sides must be greater than the third side
  • The difference of 2 sides must be less than the third side
  • The longest side of the triangle is opposite the largest angle
  • The shortest side of the triangle is opposite the smallest angle
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16
Q

Isosceles Triangle
- relationship between sides and angles
- altitude is also?

A
  • 2 ≅ sides and 2 ≅ base angles
  • The altitude drawn from the vertex is also the median and
    angle bisector
  • If two sides of a triangle are ≅, then the angles opposite
    those ≅ sides are ≅.
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17
Q

Side-Splitter Theorem

A

If a line is parallel to a side of a triangle and intersects the other two sides, then this line divides those two sides proportionally.

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18
Q

Triangle Congruence Theorems

A

SSS
SAS
ASA
AAS
HL

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19
Q

CPCTC

A

Corresponding Parts of Congruent Triangles are Congruent

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20
Q

Similar Triangle Theorems

A

AA
SAS
SSS

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21
Q

Similar figures have

A

Similar figures have congruent angles and proportional sides

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22
Q

Similar-Proportional Sentence

A

Corresponding Sides of Similar Triangles are Proportional

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23
Q

means/extremes

A

In a proportion, the product of the means equals the product of the extremes

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24
Q

Geometric Mean

A

multiply numbers together, take the square root

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25
Q

Altitude Theorem

A

The altitude is the geometric mean between the 2 segments of the hypotenuse.

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26
Q

Leg Theorem

A

The leg is the geometric mean between the segment it touches and the whole hypotenuse.

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27
Q

Reflection

A

r

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28
Q

Rotation

A

R

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29
Q

Translation

A

T

30
Q

Dilation

A

D

31
Q

r(x-axis) (x, y)

A

(x, -y)

32
Q

r(y-axis) (x, y)

A

(-x, y)

33
Q

r(y=x) (x, y)

A

(y, x)

34
Q

r(y=-x) (x, y)

A

(-y, -x)

35
Q

r(0, 0) (x, y)

A

(-x, -y)

36
Q

R(90) (x, y)

A

(-y, x)

37
Q

R(180) (x, y)

A

(-x, -y)

38
Q

R(270) (x, y)

A

(y, -x)

39
Q

T(a,b) (x, y)

A

(x+a, y+b)

40
Q

D(k) (x, y)

A

(kx, ky)

41
Q

rigid motions preserve

A

distance, congruency, and angle measures

42
Q

Rotational Symmetry

A

(360/n)

43
Q

Circle Equation

A

(x-h)^2 + (y-k)^2 = r^2

44
Q

Central Angle

A

<x = AB

45
Q

Inscribed Angle

A

<x = 1/2(AB)

46
Q

Tangent-Chord Angle

A

<x=1/2(AB)

47
Q

Two Chord Angles

A

<x = (arc1+arc2)/2

48
Q

Two Secants

A

(Whole)(External) = (Whole)(External)

49
Q

(Secant, Tangent)

A

(Whole)(External) = Tangent^2

50
Q

Area of Sector (Radians)

A

A = (1/2)r^2(angle-in-radians)

51
Q

Area of Sector (Degrees)

A

A = (n/360)(π)(r^2)

52
Q

Sector Length

A

s = r(angle-in-radians)

53
Q

Mass

A

(Density)(Volume)

54
Q

Density

A

Mass/Volume

55
Q

Quadrilateral

A

four-sided polygon

56
Q

Trapezoid

A

at least one pair of parallel sides

57
Q

Median of a Trapezoid

A

1/2(Base1+Base2)

58
Q

Isosceles Trapezoid

A
  • each pair of base angles are congruent
  • diagonals are congruent
  • one pair of congruent sides (which are the called the legs. These are the non-parallel sides)
59
Q

Parallelogram

A
  • opposite sides are parallel
  • opposite sides are congruent
  • opposite angles are congruent
  • consecutive angles are supplementary
  • diagonals bisect each other
60
Q

Rectangle

A
  • all angles at its vertices are right angles
  • diagonals are congruent
61
Q

Rhombus

A
  • all sides are congruent
  • diagonals are perpendicular
  • diagonals bisect opposite angles
  • forms four congruent right triangles
  • forms two pairs of two congruent isosceles triangles
62
Q

Square

A
  • diagonals form four congruent isosceles right triangles
63
Q

Scale Factor (Similarity)

A

original/new

64
Q

Scale Factor (Dilation)

A

new/original

65
Q

Degree to Radian

A

π/180

66
Q

Radian to Degree

A

180/π

67
Q

Total Population

A

Population Density * Area

68
Q

median

A

bisects the opposite side from vertex
centroid

69
Q

angle bisector

A

incenter

70
Q

altitude

A

orthocenter

71
Q

perpendicular bisectors

A

bisect the side w/o the vertice connect
circumcenter

72
Q

Find the slope of a perpendicular bisector

A

find midpont, substitute given into y=mx+b

2022-2023 (29 decks)

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