Geometry Regents Review Flashcards by Aarushi Arora

Sum of Interior Angles

180 (n - 2)

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Each Interior Angle of a Regular Polygon

(180(n-2))/n

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Sum of Exterior Angles

360

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Each Exterior Angle

360/n

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

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

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Standard Form of a Line

y=mx+b

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Slope Formula

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

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Parallel Lines

same slope, different y-intercepts

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Perpendicular Lines

negative reciprocal slopes

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Collinear Points

same line

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Midpoint Formula

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

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Distance Formula

d = √(x2 − x1)^2 + (y2 − y1)^2

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New X-Coordinate

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

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New Y-Coordinate

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

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

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

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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Side-Splitter Theorem

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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Triangle Congruence Theorems

SSS
SAS
ASA
AAS
HL

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CPCTC

Corresponding Parts of Congruent Triangles are Congruent

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Similar Triangle Theorems

AA
SAS
SSS

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Similar figures have

Similar figures have congruent angles and proportional sides

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Similar-Proportional Sentence

Corresponding Sides of Similar Triangles are Proportional

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means/extremes

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

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Geometric Mean

multiply numbers together, take the square root

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Altitude Theorem

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

Leg Theorem

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

Reflection

Rotation

Translation

Dilation

r(x-axis) (x, y)

(x, -y)

r(y-axis) (x, y)

(-x, y)

r(y=x) (x, y)

(y, x)

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

(-y, -x)

r(0, 0) (x, y)

(-x, -y)

R(90) (x, y)

(-y, x)

R(180) (x, y)

(-x, -y)

R(270) (x, y)

(y, -x)

T(a,b) (x, y)

(x+a, y+b)

D(k) (x, y)

(kx, ky)

rigid motions preserve

distance, congruency, and angle measures

Rotational Symmetry

(360/n)

Circle Equation

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

Central Angle

Inscribed Angle

Tangent-Chord Angle

Two Chord Angles

Two Secants

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

(Secant, Tangent)

(Whole)(External) = Tangent^2

Area of Sector (Radians)

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

Area of Sector (Degrees)

A = (n/360)(π)(r^2)

Sector Length

s = r(angle-in-radians)

Mass

(Density)(Volume)

Density

Mass/Volume

Quadrilateral

four-sided polygon

Trapezoid

at least one pair of parallel sides

Median of a Trapezoid

1/2(Base1+Base2)

Isosceles Trapezoid

- 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)

Parallelogram

- opposite sides are parallel - opposite sides are congruent - opposite angles are congruent - consecutive angles are supplementary - diagonals bisect each other

Rectangle

- all angles at its vertices are right angles - diagonals are congruent

Rhombus

- all sides are congruent - diagonals are perpendicular - diagonals bisect opposite angles - forms four congruent right triangles - forms two pairs of two congruent isosceles triangles

Square

- diagonals form four congruent isosceles right triangles

Scale Factor (Similarity)

original/new

Scale Factor (Dilation)

new/original

Degree to Radian

π/180

Radian to Degree

180/π

Total Population

Population Density * Area

median

bisects the opposite side from vertex centroid

angle bisector

incenter

altitude

orthocenter

perpendicular bisectors

bisect the side w/o the vertice connect circumcenter

Find the slope of a perpendicular bisector

find midpont, substitute given into y=mx+b