Geometry SOL Formulas

Distance Formula

\sqrt{\left(y2-y1\right)^2+\left(x2-x1\right)^2}

Midpoint Formula

\left(\frac{x1+x2}{2}\right),\left(\frac{y1+y2}{2}\right)

Slope Formula

\frac{y2-y1}{x2-x1}

Logic Symbols

Conjunction: p ^ q

Disjunction: p v q

Negation: ~p

Logic Statements

• Conditional: p →q

• Converse: q →p

• Inverse: ~p → ~q

• Contrapositive: ~q →~p

• Bi-Conditional: p if and only if q

Law of Detachment

p → q

p is true

therefore q

Law of Syllogism

p →q

q →r

therefore p →r

Law of Contrapositive

p → q

~q

therefore ~p

45 Degree Special Right Triangle

sides are a

Hypotenuse is a \sqrt2

30/60/90 Special Right Triangle

Shortest side is a

Long side is a \sqrt3

Hypotenuse is 2a

Trig

SOH-CAH-TOA

Finding Missing Side in Trig

sin38=17/x

In calculator: x=17/sin38

Finding Missing Angle in Trig

cos of theta=4.4/11

In calculator: cos-1(4.4/11)

Interior Angle Formulas

Sum: 180(n-2)

One Angle: 180(n-2)/n

Exterior Angle Formulas

Sum: 360

One Angle: 360/n

Angles in Circle

Central Angle: Equal to arc

Inscribed Angle: Half of arc

Arc Length

\frac{x}{360}\cdot2\pi r

Area of a Sector

\frac{x}{360}\cdot\pi r^2

Equation of a Circle

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

h, k is center of circle

r is radius