Geometry Regents Formulas Flashcards
Midpoint Formula
(x¹ + x²)/2, (y¹ + y²)/2.
Point-Slope Formula
y-y₁=m(x-x₁)
Distance Formula
√(x₂ - x₁) ² + (y₂ - y₁)²
Slope Formula
y₂ - y₁/x₂ - x₁
Pythagorean Converse: a²+b²=c²
Right Triangle
Pythagorean Converse: a²+ b² > c²
Acute Triangle
Pythagorean Converse: a²+ b² < c²
Obtuse Triangle
sin
opposite/hypotenuse
cos
adjacent/hypotenuse
tan
opposite/adjacent
Opposite
What the angle is facing
Adjacent
Next to the angle put not the hypotenuse
Hypotenuse
Doesn’t form a perpendicular angle
Elevation
If the triangle is going up
Depression
If the triangle is going down
Slope Intercept Formula
y=mx+b
Same Side Interior Angles
Are supplementary angles, are congruent, and on the same side
Average Speed
Distance/Time
What is the Pythagorean Theorem used for?
To find a missing right triangle side length
Reflection over the x axis
(x,y) -> (x,-y)
Reflection over the y axis
(x,y) -> (-x,y)
Reflection y=x
(x,y) -> (y,x) (goes diagonally to the right)
Reflection y=-x
(x,y) -> (-y, -x) (goes diagonally to the left)
Rotation 90 Degrees Counterclockwise or 270 degrees clockwise
(x,y) -> (-y, x)
Rotation 180 Degrees Counterclockwise or 180 degrees clockwise
(x,y) -> (-x, -y)
Rotation 270 Degrees Counterclockwise or 90 degrees clockwise
(x,y) -> (y,-x)
What way do you work with transformation when you see a ° symbol
Work the transformations from right to left
General/Standard Equation of a Circle:
x² + y² + Cx + Dy + E = 0
Center – Radius Equation of a Circle:
(x-h)²+(y-k)²=r²
Central Angle:
A piece from the center of a circle the arc and angle with be in the same degrees
Inscribed Angle:
An angle from the end of a triangle, the angle will be half of the arc’s angle
Tangent-Chord Angle:
has a line inside the circle and outside of the circle ∠x =(1/2) arc AB
If the angle is outside of the circle but forms in the circle
(big arc - little arc)/2 = ∠x
Two Cord Angle
Angle inside a circle when to lines inside the circle bisect
Formula: Arc¹ + Arc²/2
Mass
Density times Volume
Density
Mass/Volume
Cross Section
A shape making a cut into another shape
What is a quadrilateral
A four shaped shape
Trapezoid
At least one pair of parallel sides
Consecutive Angles
Angles on the same line that add up to 180 degrees
Median
A line from the vertex to the midpoint
Circumference Formula
2πr
Circumference
Distance Around A Circle
Arc Formula
πrθ/180
Secant
a line that intersects a circle at two points
Tangent
is a line that intersects a circle at on point
Sector
A portion of a circle
How to find the area of a sector
(θ/360)πr²
How to find a point on a line when they give a ratio of the segments
x₁+(a/a+b)(x₂-x₁)
–> For X Coordinate
y₁+(a/a+b)(y-y₁))
–> For Y Coordinate
Combine the X and Y to get the point on a line
When do you use point slope formula
When you only have one point that you need to find the slope and y intercept of.
