Formula Chart for Geometry on the SBAC Test

Geometry is literally everywhere! It’s in the shape of the stars and planets, in the food you eat, in your smartphone, and even in the icons for the apps in your smartphone. All the different shapes in the universe can be described by formulas and equations, and for Geometry on the SBAC Test, you need to know how to handle those formulas. The following chart is intended for study purposes only, as you won’t be able to use it during the actual test, but is really helpful to learn how to handle them when solving Geometry problems on the SBAC Test!

You can find free practice for the SBAC at Union Test Prep.

And you can find our other four formula charts for this test here:

Algebra

Functions

Number and Operations

Statistics and Probability

Geometry Formulas for the SBAC

Category	Formula	Symbols	Comment
Transformations	\((x,y)\rightarrow(x, -y)\)	Reflection x-axis
Transformations	\((x,y)\rightarrow(-x, y)\)	Reflection y-axis
Transformations	\((x,y)\rightarrow(-x, -y)\)	Reflection Origin
Transformations	\((x,y)\rightarrow(y, x)\)	Reflection line y = x
Transformations	\((x,y)\rightarrow(-y, -x)\)	Reflection line y = -x
Transformations	\((x,y)\rightarrow(y, -x)\)	Rotation \(90^o\) Counterclockwise
Transformations	\((x,y)\rightarrow(-x, -y)\)	Rotation \(180^o\) Counterclockwise
Transformations	\((x,y)\rightarrow(x+a, y+b)\)	Translation
Transformations	\((x,y)\rightarrow(rx, ry)\)	Dilation (r = scale factor)
Right Triangles	\(a^2+b^2=c^2\)	a, b = legs of a right triangle c = hypotenuse of a right triangle	Pythagorean Theorem
Coordinates	\(y = m \cdot x + b\)	y = dependent variable m = slope x = independent variable b = y-axis intercept	Slope-Intercept Form of a line: Try to convert any given linear equation to this form.
Coordinates	\(m= \frac{(y_2-y_1)}{(x_2-x_1)}\)	\(m\) = slope \(y_n\) = dependent variable at point n \(x_n\) = independent variable at point n	This is a rearranged version of the point-slope form.
Coordinates	\(y-y_1=m(x-x_1)\)	\((x_1, y_1)\) = point on the line y = dependent variable x = independent variable m = slope	Point-slope form of a line
Coordinates	\(d=\sqrt{(y_2-y_1)^2 +(x_2-x_1)^2}\)	d = distance between two points \(y_n\) = y value at point n \(x_n\) = x value at point n
Coordinates	\((x_m, y_m) = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\)	\(x_m\) = x value at the midpoint \(y_m\) = y value at the midpoint \(y_n\) = y value at point n \(x_n\) = x value at point n
Volume	\(V=l \cdot w \cdot h\)	V = volume of rectangular prism l = length w = width h = height
Volume	\(V = \frac{1}{3} \cdot l \cdot w \cdot h\)	V = volume of pyramid l = length w = width h = height
Volume	\(V = \pi \cdot r^2 \cdot h\)	V = volume of a cylinder r = radius h = height
Volume	\(V= \frac{4}{3} \cdot \pi \cdot r^3\)	V = volume of a sphere r = radius
Circles	\(C = 2 \cdot \pi \cdot r\) \(C = \pi \cdot d\)	C = circumference (perimeter) r = radius d = diameter \(\pi\) = 3.14
Circles	\(s = r \cdot \theta\)	s = arc length r = radius \(\theta\) = central angle (radians
Circles	\(A = \pi \cdot r^2\)	A = area of a circle r = radius
Conic Sections	\((x-h)^2 + (y-k)^2 = r^2\)	\((h, k)\) = center of circle r = radius	Standard form of a circle
Conic Sections	\((x-h)^2 = 4p \cdot (y-k)\)	\((h, k)\) = vertex of a parabola p = distance from vertex to directrix	Parabola that opens up or down
Conic Sections	\((y-k)^2 = 4p \cdot (x-h)\)	\((h, k)\) = vertex of a parabola p = distance from vertex to directrix	Parabola that opens left or right
Shapes	\(A=\frac{1}{2} \cdot b \cdot h\)	A = area of a triangle b = base h = height
Shapes	\(A = s^2\)	A = area of a square s = side length
Shapes	\(A=l \cdot w\)	A = area of a rectangle l = length w = width
Shapes	\(A=h \cdot \frac{(b_1+b_2)}{2}\)	A = area of a trapezoid \(b_n\) = base n h = height

Trigonometry

\[sin\ \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac {1}{ csc\ \theta}\] \[cos\ \theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac {1}{ sec\ \theta}\] \[tan\ \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac {1}{ cot\ \theta}\]