Geometry Regents Review Flashcards
Sum of Interior Angles
180 (n - 2)
Each Interior Angle of a Regular Polygon
(180(n-2))/n
Sum of Exterior Angles
360
Each Exterior Angle
360/n
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
Standard Form of a Line
y=mx+b
Slope Formula
m=(y2-y1)/(x2-x1)
Parallel Lines
same slope, different y-intercepts
Perpendicular Lines
negative reciprocal slopes
Collinear Points
same line
Midpoint Formula
M = (((x1+x2)/2), ((y1+y2)/2)))
Distance Formula
d = √(x2 − x1)^2 + (y2 − y1)^2
New X-Coordinate
x1+(r1/(r1+r2))(x2-x1)
New Y-Coordinate
y1+(r1/(r1+r2))(y2-y1)
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
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 ≅.
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.
Triangle Congruence Theorems
SSS
SAS
ASA
AAS
HL
CPCTC
Corresponding Parts of Congruent Triangles are Congruent
Similar Triangle Theorems
AA
SAS
SSS
Similar figures have
Similar figures have congruent angles and proportional sides
Similar-Proportional Sentence
Corresponding Sides of Similar Triangles are Proportional
means/extremes
In a proportion, the product of the means equals the product of the extremes
Geometric Mean
multiply numbers together, take the square root
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
r
Rotation
R
Translation
T
Dilation
D
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
<x = AB
Inscribed Angle
<x = 1/2(AB)
Tangent-Chord Angle
<x=1/2(AB)
Two Chord Angles
<x = (arc1+arc2)/2
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
